MANUAL  OF  ADMEASUREMENT. 

THE 

UNITED     STATES 

TONNAGE  LAW  OF  1864, 

WITH  AN  ANALYSIS  OF  THE 

P0k  of  measuring  UJips  mft  fes&els, 

ILLUSTRATED    BY 

FORMULAE,  DIAGRAMS,  AND  FULL  DIRECTIONS  FOR  THE  AD- 
MEASUREMENT OF  VESSELS  OF  ALL  FORMS  AND  SIZES  ;  WITH 
EXAMPLES  OF  ITS  APPLICATION  TO  THE  PURPOSES  OF  NA- 
VAL ARCHITECTURE,  AS  WELL  AS  TO  THE  CUBATURE  OF 

ALL   BODIES    OF   WHATEVER    CONFIGURATION,    &C.,    &C. 


BY    I.     R.     BUTTS, 
// 

Author  of  the  "United  States  Business  Man's  Law  Cabinet";  "The  Mer- 
chant's and  Shipmaster's  Manual  and  Shipbuilder's  and  Sailmaker's 
Assistant"  ;  "  Laws  of  the  Sea"  \  &c.  &c. 


BOSTON: 

PUBLISHED    BY  L.E    BUTTS    &    CO., 

CORNER   OF  SCHOOL  AND  WASHINGTON  STREETS. 
1865. 


[From  the  Hon.  J.  Z.  Goodrich,  Collector  for  the  Port  of  Boston."} 

CUSTOM  HOUSE,  BOSTON. 
Collector's  Office,  12th  Dec.,  1864. 
Messrs.  I.  R.  BUTTS  &  Co. 

Gentlemen, — I  have  sent  the  copy  of  the  Manual 
of  Admeasurement,  you  handed  me,  to  the  Treasury  Department. 
The  work  has  been  examined  in  this  Office,  and  is  regarded  as  a 
useful  adjunct  in  execution  of  the  new  system  of  Admeasurement. 
The  introduction  and  demonstration  are  exceedingly  valuable,  the 
latter  making  the  reason  of  the  rule  clear,  so  that  once  understood 
it  can  never  be  forgotten,  or  incorrectly  applied. 
Yours  resp'y, 

J.  Z.  GOODRICH. 

[From  the  Hon.  G.  V.  Fox,  Assistant  Secretary  of  JVavy.~\ 

WASHINGTON,  Dec.  12,  1864. 
I.  R.  BUTTS  &  Co., 

Dear  Sirs, — I  thank  you  for  the  little  book  on  Ton- 
nage. It  seems  to  be  very  accurate,  and  is  necessary  to  enable  our 
people  to  avail  themselves  readily  of  the  new  law. 

Very  faithfully, 

G.   V.  FOX. 

[From  Sam'l  H.  Pooky  Naval  Architect.} 

FAIR  HAVEN,  Dec.  13,  1864. 
Messrs.  I.  R.  BUTTS  &  Co. 

Dear  Sirs, — Your  favor  enclosing  copy  of  Ton- 
nage Law  was  duly  received,  for  which  I  am  much  obliged. 

It  seems  to  be  a  work  which  will  be  much  needed  by  all  Nautical 
men,  Ship-owners,  and  Ship-builders. 

With  respect,  your  obed't  Servant, 

SAM'L  H.   POOK. 


Entered,  according  to  Act  of  Congress,  yi  the  year  1S65,  by  I.  R.  BUTTS,  in  the 
Clerk's  Office  of  the  District  Court  of  the  District  of  Massachusetts. 


CONTENTS. 


DEMONSTRATION  OF  THE  RULE  FOR  MEASURING  AREAS- 

Page 

M.  PONCELET'S  Demonstration  of  the  Formula  used  in  Shipbuilding 
to  express  an  Area  bounded  by  a  Straight  and  Curved  Line,     7 

PRISMOIDAL  FORMULA. 

To  find  the  Solidity  of  a  Cone,— of  a  Wedge,— of  a  Sphere,  — of 
a  Hemisphere,  —  and  of  other  Solid  bodies, 9 

INTRODUCTORY    REMARKS, 
£*       Explanatory  of  the  Law  for  the  Admeasurement  of  Vessels, .....  11 

AN    ACT  TO  REGULATE  THE  ADMEASUREMENT  OF    TON- 
z  3  NAGE   OF   SHIPS  AND  VESSELS  OF  THE  U,  S. 

•    Vessels  when  to  be  Measured  and  Remeasured, 15 

>  %   Register  of  Vessel,  what  shall  express 15 

?    Tonnage  of  Vessel  derived  from  Cubic  Content, , 16 

•  jJJ    Length  how  taken  and  Number  of  Divisions, 16 

^  u:    Table  of  Classes. — Method  of  finding  the  Areas, 17 

O  °   Metnod  of  ascertaining  the  Register  Tonnage  of  Vessel, 19 

Measurement  of  the  Poop  and  other  closed-in  Space, 19 

Measurement  of  the  Third  or  Spar  Deck, 20 

Tonnage  of  Open  Vessels  how  ascertained, 21 

Registered  Tonnage  to  be  Carved  on  the  Main  Beam, 21 

Charge  for  Measuring  and  Certificate, 22 

Act  not  to  apply  to  Vessels  not  required  to  be  Registered  or  En- 
rolled,  , 22 

ANALYSIS  OF  THE  MODE  FOR  THE  ADMEASURE- 
MENT OF  TONNAGE. 

PLAN  BASED  ON  INTERNAL  CAPACITY, 23 

English  Table  of  Areas  or  Sections  (note) ". 28 

The  Tonnage  bas.ed  on  internal  capacity,  affords  an  immediate 

knowledge  of  the  Size  of  a  Vessel, 24 

Disadvantages  of  External  Measurement, 24 

Advantages  of  Internal  Measurement, 24 

RULE  FOR  DETERMINING  THE  REGISTER  TONNAGE, 25 

Outline  of  Mode, 25 


CONTENTS. 


Page 

GENERAL  PROCESS  FOR  FINDING  AN  AREA,  &c., 25 

Example  of  the  Measurement  of  an  Area, 25 

Diagram  of  an  Area 26 

General  Formula  for  Computing  an  Area,   26 

Cubical  Content  under  the  Tonnage-deck  how  obtained, 27 

Example  of  computing  the  Cubical  Content  below  the  Tonnage- 
deck  by  means  of  the  Transverse  Areas, 27 

Diagram  of  a  Vessel  divided  into  Areas  or  Sections, 27 

General  Formula  for  Computing  the  Tonnage  below  the  Tonnage- 
deck,  28 

CORRECTNESS  OF  PROCESS  PROVED  BY  EXAMPLES, 28 

Ex.  1. — Parallelogrammical  or  Wall-sided  Form, 29 

Measurement  by  Tonnage  Rule  and  Measurement  by  Geometry,  29 

Ex.  2.— Circular  Form, 30 

Measurement  by  Tonnage  Rule,  and  Measurement  by  Geometry,  30 

Ex.  3.— Parabolic  Form, 31 

Measurement  by  Tonnage  Rule,  and  Measurement  by  Geometry,  31 

Ex.  4. — Triangular  or  Wedge-like  Form, 31 

Measurement  by  Tonnage  Rule,  and  Measurement  by  Geometry,  32 

TONNAGE  OF  THE  SPACES  ABOVE  DECK, , 33 

Measurement  of  the  Poop. — Example  of  Computation. — Formula,  33 

Measurement  of  Forecastle. — Example  of  Computation/. 34 

SPAR  AND  TONNAGE- DECKS, , 35 

Measurement  of  the  Space  between  the  Spar  and  Tonnage-decks 

in  Vessels  having  a  Spar  or  Third  Deck, 35 

Example  of  Computation  — General  Formula, ^ . .   36 

DIRECTIONS  FOR   TAKING  THE  MEASUREMENTS  OP 

VESSELS. 

Length, 37 

Points  of  Division, 37 

Depths, 38 

Breadths, 38 

Remarks, 38 

DIAGRAM    OF    A    MIDSHIP    AREA    SHOWING    THE 
BREADTHS. 

Description  of  the  Breadths,  also,  their  Position  in  relation  to  the 

Depths,  when  the  Midship  Depth  does  not  exceed  16  feet, ...  39 

References  to  Plate, 39 

Remarks, 39 

MEASURING    SURVEYOR'S    FORMULA. 

Blank  Formula  for  the  use  of  the  Measuring  Surveyor,  in  the 

Practical  Operation  of  the  Admeasurement  of  Vessels 41 

General  Formula  for  the  use  of  the  Measuring  Surveyor, 42 


CONTENTS.  t  D 

ESSENTIAL    QUALITIES    OF    THE   LAW. 

Page 

The  Evasion  of  Lawful  Tonnage  prevented, 43 

Inducement  to  construct  ill-formed  Vessels  removed, 43 

Tonnage  in  proportion  to  capacity  obtained, 43 

"Wrong  Measurement  can  be  detected, 43 

Cubic  Feet  in  Hold  ascertained, 44 

Measurement  of  Cargo  ascertained, 44 

Weight  of  Cargo  ascertained, 44 

PROPORTIONS  OF  SHELLS  OF  SHIPS  TO  THEIR    IN- 
TERNAL   CAPACITIES. 

Tables  and  Remarks  connected  with  the  thickness  of  the  Sides  or 
Shells  of  Vessels  built  of  different  materials,  as  Oak,  Fir, 

and  Iron, 45 

Table  No.  1 45 

Medium  thickness  of  the  sides  of  Oak,  Fir  and  Iron  Vessels, 46 

Table  No.  2, 46 

Remarks  on  the  Results  in  the  preceding  Tables,  Nos.  1  and  2. . .  46 
More  Timber  in  'the  frames  of  long  sharp  Vessels  than  in  short 

full  ones  of  equal  tonnage, 47 

In  the  usual  form  of  Vessels,  the  larger  the  Vessel  the  less  Timber 

in  the  frame  in  proportion  to  tonnage, 47 

Timber  in  the  frame  of  a  Vessel  approximately  estimated, 47 

Examples  of  finding  the  quantity  of  Timber  in  the  frame, 48 

Advantages  of  correct  Admeasurement  in  affording  means  of  prac- 
tical Estimates 49 

EXTERNAL    MEASUREMENT,    AN    ADVANTAGE    TO 
THIN-SIDED    VESSELS. 

Table  No.  3, 50 

Advantage  of  Oak  over  Fir  Vessels  by  External  Measurement, ...  50 

Advantage  of  Iron  over  Oak  Vessels  by  External  Measurement, . .  50 

Advantage  of  Iron  over  Fir  Vessels  by  External  Measurement, . .  60 
Synopsis  of  the  advantages  which  thin-sided  vessels  have  over 

thick-sided  vessels, 51 

Table  No.  4, 52 

WEIGHTS    OF    THE    HULLS    OF    IRON    AND    WOOD- 
BUILT    VESSELS   COMPARED. 
Table  No.  5 53 

In  steam-vessels  iron  hull  more  buoyant  than  wood  hull, 54 

Difference  in  Scantling  allowed  in  steam- vessels, 54 

In  sailing-vessels,  iron  hull  more  buoyant  than  in  steam-vessels,  54 

Practical  conclusions  deduced  from  preceding  results, 55 

Additional  cargo  carried  by  sailing-vessels  built  of  iron, 55 

Additional  cargo  carried  by  steam-vessels  built  of  iron, 55 

Bl  1* 


6  CONTENTS. 

FORMULA 

Page 

To  Approximate  Register  Tonnage  under  any  proposed  principal 
Dimensions  , 56 

RULE  TO   ASCERTAIN  THE   MEASUREMENTS   AND    DEAD- 
WEIGHT   CARGO    OF    SHIPS. 

A  brief  Explanation  of  the  Nature  of  the  Register  Tonnage  of  a 
Ship  as  ascertained  under  the  "  Merchant's  Shipping  Act, 
1854  " ;  and  of  the  easy  means  it  affords  for  estimating,  ap- 
proximately, the  Measurements  and  Deadweight  Cargo  of 
Ships, 56 

Table, 59 

CENTRE    OF    GRAVITY    OF    DISPLACEMENT. 

Method  of  ascertaining  the  Centre  of  Gravity  of  the  Displacement 
of  a  Vessel,  founded  upon  the  same  general  Process  as  the 

Rule  for  determining  the  Register  Tonnage, . . .  4 60 

Remarks  on  the  position  on  the  centre  of  gravity  of  displacement,  60 

General  theorem  in  reference  to  the  centre  of  gravity, 61 

Equation  for  finding  the  distance  of  the  centre  of  gravity  of  dis- 
placement from  Area  No.  1,  measured  on  load-water  line,. . .  62 
General  Formula  for  finding  the  Centre  of  Gravity  of  Displace- 
ment, supposing  the  Areas  of  the  Sections  to  be  already  found,  63 
Position  of  the  Centre  of  Gravity  of  Displacement  below  load- 
water  line, 63 

LOAD    DISPLACEMENT    OF   A    VESSEL. 

Method  of  finding  the  Load  Displacement  of  a  Vessel,  by  means  of 

the  Formula  for  the  Admeasurement  of  Tonnage, 64 

Load  Displacement  determined  with  the  greatest  nicety, 64 

CUBATURE  OF  BODIES  OF  WHATEVER  CONFIGURATION, 
Cubature  of  the  Pyramid,- 65 

General  Formula  for  Cubature  Three  Transverse  Areas  being  given,  66 
To  find  the  Position  of  the  Centre  of  Gravity  of  the  Pyramid, ....  67 
General  Formula  for  finding  the  Distance  of  the  Centre  of  Gravity 

from  Area  No.  1,  Three  Transverse  Areas  being  given, 67 

General  Process  applied  to  the  Measurement  of  a  piece  of  Timber,  67 
Measurement  by  General  Process, — General  Formula, *  68 


DEMONSTRATION 

OP  THE 

RULE  FOR  MEASURING  AREAS, 


The  formula  commonly  used  in  Shipbuilding,  to  ex- 
press an  area  bounded  by  a  straight  line  arid  a  curved 
line,  is  as  follows : —  . 


Area=      A  +  4P  +  2Q  -, 


where  A  —  Sum  of  first  and  last  ordinates. 
P  —  Sum  of  even  ordinates. 
Q  —  Sum  of  odd  ordinates. 
r  —  Common  distance  between  ordinates, 
The  whole  number  of  ordinates  being  odd,  and   the 
number  of  intervals  being  even. 

The  most  simple  demonstration,  perhaps,  is  the  follow- 
ing, given  by  M.  PONCELET  in  his  "  Mecanique  Indus- 
trielle." 


Let  AabcC  be  a  por- 
tion of  the  area  included 
between  the  curve  abc,  the 
line  AC  consisting  of  tivoa, 
of  the  common  intervals  r 
and  the  ordinates  Aa,  Cc : 
there  being  one  intermedi- 
ate ordinate  Eb. 

Divide  AC  into  3  equal 
portions  in  D  and  E.  So 
that 


D B 


AD  =  DE  =  EC  =  J 


—  2r 

At  D  and  E  erect  ordinates  ~Dd,  ~Ke.     Draw  the  chords  ad3 
de,  and  ec ;  let  de  cut  Bd  in  /?. 

Then  evidently,  if  the  points  a,  b,  c,  be  taken  sufficient- 
ly near,  the  area  abcCA  will  be  very  approximately 
represented  by  the  sum  of  the  three  trapezia  Ad,  De,  and 


8 


DEMONSTRATION    OP   THE 


EC,  the  difference  being  the  three  spaces  included  be- 
tween the  curve  abc,  and  the  chords  ad,  de,  and  ec,  which 
are  of  no  appreciable  magnitude  compared  with  the 
whole  area.  Now  the  area  of  a  trapezium  having  two 
sides  parallel  =:  £  (the  sum  of  the  parallel  sides)  X  per- 
pendicular distance  between  them. 

.  •  .  Area  trapezium  Ad  —  £(Aa  -)-  DC?)  AD. 


EC  =.  4(Ee  +  Cc)  EC. 

.  '  .  Approximately  the  area  AabcC  =  ^-\Aa  -f-  2Dd  -\- 

2Ee  +  Cc)  AD 
•  .  •  AD  =  DE  =  EC. 

Now  De?  +  Ee  =±  2B#,  as  may  be  easily  proved  .  •  .  2De? 
-f  2Ee  =  4B|5  =±  4  B6  •  .  •  B0  differs  from  Bb  only  by  60, 
which  is  of  inappreciable  magnitude  compared  with  B£  : 
hence  calling  Aa,  B6,  Cc,  ait  0%,  and  a3  respectively,  and 


putting  for  AD  its  value 


2r 

AC  or  —  we  have 
o 

2r 


Area  AabcC  =  £  {  ax  +  4a2  +  «3)  X  --  =  («i  +  4«2  +  a3)- 


ABCDEFHKL 

Let  now  the  whole  area  whose  magnitude  is  required  be 
divided  into  any  number  of  intervals  similar  to  AabcC, 
i.  e.  into  any  even  number  of  spaces,  having  therefore  an 
odd  number  of  ordinates ;  the  common  interval  being  rt  as 
in  the  figure,  and  let  the  ordinates 

Aa,  B6,  Cc,  Dd,  &c.,  be  alt  0%,  a3t  a±, a 


RULE    FOR   MEASURING   AREAS.  CJ 

T 

Then  area  CceE  =  (<z3,  +  4ait  +  «5)— 

o 

also  Ee/iH  =  (as,  +  4a6,  +  «7)^- 

&c.  &c. 

Adding,  we  obtain 

whole  area  =  (^  +  4a2  +  2a2  +  4a4  +  2a5  +  &  +  a)— , 

I    o 


=  (A  +  4P  +  2Q). 


PRISMOIDAL    FORMULA. 

The  following  Rules  for  Solid  Mensuration,  from  the  <(  Franklin 
Journal,"  illustrate,  by  a  very  simple  method,  the  Rule  for  Meas- 
uring Areas. 

The  leading  rules  of  solid  mensuration,  laid  down  in  the  books, 
separate  rules  being  given  for  each  solid,  are  the  following,  every  one 
of  which  may  be  superseded  by  the  Prismoidal  Formula. 

To  find  the  solidity  of  a  Cube  ;  Parallelopipedon  ;  Prisms  ;  Cones  ; 
Cylinders  ;  Pyramids  ;  Frustum  of  Cone  ;  Frustum  of  Pyramid  ;  Pris- 
moid  ;  Wedge  ;  Sphere. 

A  number  of  other  special  rules  are  given  for  the  solidity  of  spher- 
oids, paraboloids,  and  other  solids  of  revolution,  their  spindles  and 
segments  ;  to  many  of  which  the  prismoidal  formula  is  applicable. 


By  the  Special  Rules  of  the  Books. 

To  find  the  solidity  of  a  Cone. 

RULE.  —  Multiply  the  area  of  the  base 
by  the  height,  and  one-third  of  the  pro- 
duct will  be  the  solidity. 

Given.  —  A  cone  having  a  diameter  at 
the  base  of  2,  a  mid  diameter  of  1,  and 
a  height  of  6.    Query:  The  solidity  ? 
2  X  2  X  -7854  =  3.1416 


3)18.8496 


Solidity  =  6.2832 


By  Prismoidal  Formula. 

The  Prismoidal  Formula  is, —  Add 
into  one  sum  the  areas  of  the  two  ends, 
and  four  times  the  middle  section  par- 
allel to  them ;  then  this  sum  multiplied 
by  one-sixth  of  the  height  will  give  the 
solidity. 

In  the  case  of  the  cone  opposite,  the 
diameter  of  the  base  being  2,  and  of 
the  mid   section  1,  we  have,  by  the 
prismoidal  formula, 
Base,  2  X  2  X  -7854  =  3.1416 

4  times 

mid  sec.  1  X  1  X  -7854  X  4  =  3.1416 
Top  =  0. 

1.6th  ht.  =  1.  X  6  2832 

Solidity  =  6.2832 


10 


PRISMOIDAL    FORMULA. 


To  find  the  solidity  of  a  Wedge. 

RULE. — To  the  length  of  the  edge, 
add  twice  the  length  of  the  back  ;  mul- 
tiply this  sum  by  the  height  of  the 
wedge,  and  then  by  the  breadth  of  the 
back:  one-sixth  of  the  product  will  be 
the  solidity. 

Given. — A  wedge  ;  length  of  edge  60, 
back  length  =  20,  back  breadth  =  10, 
height  100.     Query:  The  solidity? 
Length  of  edge,  =60 

Twice  back,       20  X  2  =  40 

100 
100 


10000 
10 

6)100000 
Solidity  =  16666% 


Wedge— Solidity  by  prismoidal  for- 
mula. 


Area  of  base, 
4  limes  mid  sec. 
Top 


20  X  10  =  200 

40  X  5  X  4  =  SOO 

=     0 


1000 

l-6th  ht.  =  16%  X  1000  =  16666% 
Solidity  =  16666% 


To  find  the  solidity  of  a  Sphere. 

RULE. — Multiply  the  cube  of  the  di- 
ameter by  decimal  ,5236,  the  product 
will  be  the  solidity. 

Given. — A  sphere  of  a  diameter  or 
axis  in  length  =  12.  Query :  The  solid- 
ity? 

12   X  12  X  12  X  -5236  =  904.7808  the 
solidity. 


Solidity  of  the  Sphere  opposite. 
Top  =  0. 

4  times  mid  sec. 

12  X  12  X  .7854  X  4  =  452.3904 
0. 


452.3904 

l-6thht.  =•  2  X  452.3904  =  904.780S 
Solidity  =  904.7808 


Solidity  of  a  Hemisphere. 
Take  ihe  same  dimensions  as  in  the 
sphere  above,  and  we  have— 

2)904.78 


Solidity  of  Hemisphere  =  452.39 


Solidity  of  a  Hemisphere. 
Diameter  of  mid  section  =10.392 

Diameter  of  base  =  12. 

Height  or  radius  =   6. 

Then  by  Prismoidal  Formula — 
Area  of  base  =113-097 

4  limes  mid  section 

10.392  X  10.392  X  .7854  X  4  =  339.272 
Top  =     0. 


452.369 
l-6th  ht.  =  1  X  452.369  =  452.369 

Solidity  =  452.369 

The  difference  in  the  last  decimals 
is  owing  to  too  few  decimal  places 
having  been  used  in  the  computation. 


For  the  present  purpose,  it  may  "be  sufficient  to  have  shown,  by  ac- 
tual figures,  working  out  examples  of  the  most  unpromising  cases,  the 
applicability  of  this  formula  to  compute  the  solidity  of  a  cone, 
wedge,  sphere,  and  a  hemisphere. 


INTRODUCTORY    REMARKS 

EXPLANATORY  OF  THE  NEW  LAW  FOR  THE  MEASUREMENT 
OF  SHIPPING. 

This  law  is  divided  into  five  sections,  each  on  a  separate 
and  distinct  subject.  The  first  designates  the  time  at  which 
the  law  is  to  be  enforced.  The  second  states  the  dimensions 
that  are  to  be  entered  in  the  vessel's  register,  and  designates 
the  deck  which  is  to  be  named  the  tonnage-deck.  The  third 
section  states  that  100  cubic  feet  of  internal  capacity  shall 'be 
taken  to  be  one  ton ;  it  describes  the  manner  in  which  the 
internal  measurements  are  to  be  made,  and  directs  that  the 
tonnage  calculated  as  therein  directed,  is  to  be  entered  in  the 
vessel's  register.  The  fourth  section  gives  the  tariff  of 
charges  for  making  the  measurement  and  calculating  the  ton- 
nage. The  fifth  section  repeals  all  Acts  of  Congress  that  are 
inconsistent  with  the  Act  in  question. 

The  law  provides  that  this  rule  of  measurement  shall  be  in 
force  "on  and  after  the  first  day  of  January,  1865,"  and 
that  owners  may  have  their  vessels  measured  and  registered 
under  the  new  law  at  any  time  after  the  6th  of  May,  1864 — 
the  date  of  its  approval. 

The  law  explains  in  the  clearest  possible  terms  that,  in 
vessels  having  three  or  more  decks  to  the  hull  the  second  deck 
from  below  is  to  be  the  tonnage-deck ;  in  all  other  cases,  the 


12  INTRODUCTORY   REMARKS. 

upper  deck  of  the  hull  is  to  be  the  tonnage-deck.     Steamboats 
may  have  several  decks  that  are  not  decks  to  the  hull. 

The  second  section  only  states  the  dimensions  that  are  to  be 
recorded  in  the  register  for  the  identification  of  the  vessel,  and 
which  are,  in  fact,  the  common  dimensions  in  use,  except  that 
the  breadth  of  the  stem  is  excluded  from  the  length  of  the 
vessel.  Neither  this  measure  of  length,  nor  the  other  dimen- 
sions of  extreme  breadth  or  depth  of  hold,  has  any  thing  to 
do  with  the  calculation  of  internal  capacity. 

The  law  states  that  the  length  in  the  third  section  is  not 
that  which  is  given  in  the  second  section. 

Section  third  states  how  the  internal  length  is  to  be  meas- 
ured, for  the  purpose  of  ascertaining  the  tonnage  or  internal 
capacity,  and  the  division  into  classes,  is  only  for  the  purpose 
of  determining  the  number  of  cross  sections  into  which  the 
hold  is  to  be  divided  for  this  purpose.  The  whole  subject  of 
this  section  is  the  simple  measuration  of  the  internal  capacity 
of  the  vessel  inside  of  the  ceiling  and  under  the  tonnage-deck 
plank-,  without  allowance  for  beams,  knees,  keelsons,  hooks, 
or  internal  framing  of  any  kind.  The  law  states  what  meas- 
urements are  to  be  taken  to  gauge  the  ship,  and  tells  how  the 
measurements  are  to  be  used  to  obtain  the  internal  capacity. 
Ship-builders,  who  calculate  the  displacement  of  their  vessels, 
understand  this  rule,  which  is  of  very  easy  application,  and  of 
great  accuracy. 

The  third  section  is  found  to  describe  exactly  how  the  in- 
ternal length  of  the  vessel  under  the  deck  plank  is  to  be  as- 


INTRODUCTORY    REMARKS.  13 

certained : — The  length  on  the  top  of  the  tonnage-deck,  from 
the  inside  of  the  planking  at  the  stem  to  the  inside  of  the 
planking  at  the  stern  is  measured,  and  from  that  length  is  de- 
ducted whatever  rake  there  may  be  in  the  stem  or  in  the  stern, 
in  the  thickness  of  the  deck  plank,  (the  thickness  of  the  deck 
plank  is,  generally,  only  three  or  four  inches.) 

The  Act  proceeds  to  state,  that  at  each  division  of  the 
length  of  the  vessel,  as  determined  in  the  third  section,  the 
depth  is  to  be  measured  from  a  point  at  a  distance  of  one-third 
of  the  round  of  the  beam  below  the  lower  side  of  the  deck  to 
the  limber-strake ;  the  average  thickness  is  named,  so  that  the 
depth  may  not  be  reduced  by  extraordinary  thickness  being 
given  to  the  limber-strake  alone. 

This  one-third  of  the  round  of  the  beam  is  simply  this  :  — 
An  internal  area  is  being  measured,  and  one-third  the  spring 
of  the  beam  is  very  nearly  the  mean  height,  and  the  area  under 
the  horizontal  line  at  that  mean  height,  will  be  almost  identi- 
cal with  the  actual  area,  embracing  the  whole  spring  of  the 
beam. 

It  is  at  this  mean  height  that  the  length  of  the  vessel  is 
measured. 

At  the  stem,  there  is  no  round  of  the  beam  to  be  deducted ; 

but  when  the  vessel  has  a  square  stern,  there  is  a  round  to 

the  extreme  after-end  of  the  deck ;  and  it  was  for  that  round, 

when  the   length  was  being  measured,  that  it  was  directed 

si  2 


14  INTRODUCTORY   REMARKS. 

to  deduct  ike  rake  of  the  stern  timber  in  one-third  of  the 
round  of  the  beam:  in  a  vessel  with  a  round  stern,  no 
such  deduction  is  to  be  made. 

This  rule  of  measurement  for  vessels  is  similar  to  that  of  the 
British  law,  and  there  has  been  no  difficulty  experienced 
there  in  finding  persons  to  understand  and  apply  it. 

The  old  tonnage  law  made  no  exception  for  steam  vessels, 
and  there  is  no  reason  why  there  should  be  any  in  the  present 
one.  Steamers  now  have  so  many  advantages  over  sailing 
vessels,  that  they  are  rapidly  superseding  them,  and  there  is 
no  necessity  or  good  reason  for  farther  increasing  these  ad- 


AN    ACT 


TO 


Eegulate  the  Admeasurement  of  Tonnage  of  Ships 
and  Vessels  of  the  United  States, 


VESSELS  WHEN  TO  BE  MEASURED  AND  REMEASURED. 

Be  it  enacted  by  the  Senate  and  House  of  Representatives 
of  the  United  States  of  America  in  Congress  assembkd,  That 
every  ship  or  vessel  built  within  the  United  States,  or 
that  may  be  owned  by  a  citizen  or  citizens  thereof,  on  or 
after  the  first  day  of  January,  eighteen  hundred  and  sixty- 
five,  shall  be  measured  and  registered  in  the  manner 
hereinafter  provided ;  also  every  ship  or  vessel  that  is 
now  owned  by  a  citizen  or  citizens  of  the  United  States, 
shall  be  remeasured  and  reregistered  upon  her  arrival 
after  said  day  at  a  port  of  entry  in  the  United  States, 
and  prior  to  her  departure  therefrom,  in  the  same  man- 
ner as  hereinafter  described  :  Provided,  That  any  ship 
or  vessel  built  within  the  United  States,  after  the  pas- 
sage of  this  act,  may  be  measured  and  registered  in  the 
manner  herein  provided. 

REGISTER  OF  VESSEL,  WHAT  SHALL  EXPRESS. 

SEC.  2.  And  be  it  further  enacted,  That  the  register  of 
every  vessel  shall  express  "her  length  and  breadth,  together 


16 


AN    ACT   TO    REGULATE    THE 


with  her  depth,  and  the  height  under  the  third  or  spar 
deck,  which  shall  be  ascertained  in  the  following  man- 
ner:—  The  tonnage-deck,  in  vessels  having  three  or 
more  decks  to  the  hull,  shall  be  the  second  deck  from 
below  ;  in  all  other  cases  the  upper-deck  of  the  hull  is 
to  be  the  tonnage-deck.  The  length  from  the  forepart 
of  the  outer  planking,  on  the  side  of  the  stem,  to  the  after 
part  of  the  main  stern-post  of  screw  steamers,  and  to  the 
after  part  of  the  rudder-post  of  all  other  vessels  meas- 
ured on  the  top  of  the  tonnage-deck,  shall  be  accounted 
the  vessel's  length.  The  breadth  of  the  broadest  part 
on  the  outside  of  the  vessel  shall  be  accounted  the  ves- 
sel's breadth  of  beam.  A  measure  from  the  under  side 
of  tonnage-deck  plank,  amidships,  to  the  ceiling  of  the 
hold  (average  thickness)  shall  be  accounted  the  depth  of 
hold.  If  the  vessel  has  a  third  deck,  then  the  height 
from  the  top  of  the  tonnage-deck  plank  to  the  under  side 
of  the  upper-deck  plank  shall  be  accounted  as  the  height 
under  the  spar-deck.  All  measurement  to  be  taken  in 
feet  and  fractions  of  feet ;  and  all  fractions  of  feet  shall 
be  expressed  in  decimals. 

TONNAGE  OF  VESSEL  DERIVED  FROM  CUBIC  CONTENT. 

SEC.  3.  And  be  it  further  enacted,  That  the  register 
tonnage  of  a  vessel  shall  be  her  entire  internal  cubical 
capacity  in  tons  of  one  hundred  cubic  feet  each,  to  be  as- 
certained as  follows : 

LENGTH  HOW  TAKEN  AND  NUMBER  OF  DIVISIONS. 

Lengths. — Measure  the  length  of  the  vessel  in  a  straight 
line  along  the  upper  side  of  the  tonnage-deck,  from  the 
inside  of  the  inner  plank,  (average  thickness,)  at  the  side 


ADMEASUREMENT    OF   TONNAGE.  17 

of  the  stem  to  the  inside  of  the  plank  on  the  stern  tim- 
bers, (average  thickness,)  deducting  from  this  length 
what  is  due  to  the  rake  of  the  bow  in  the  thickness  of 
the  deck,  and  what  is  due  to  the  rake  of  the  stern-tirnber 
in  the  thickness  of  the  deck,  and  also  what  is  due  to  the 
rake  of  the  stern-timber  in  one-third  of  the  round  of  the 
beam ;  divide  the  length  so  taken  into  the  number  of 
equal  parts  required  by  the  following  table,  according  to 
the  class  in  such  table  to  which  the  vessel  belongs  : 

TABLE  OF  CLASSES. 

Class  1.  Vessels  of  which  the  tonnage  length  according  to  the  above 
measurement  is  fifty  feet  or  under,  into  six  equal  parts. 

Class  2.  Vessels  of  which  the  tonnage  length  according  to  the  above 
measurement  is  above  fifty  feet,  and  not  exceeding  one 
hundred  feet  long,  into  eight  equal  parts. 

Class  3.  Vessels  of  which  the  tonnage  length  according  to  the  above 
measurement  is  above  one  hundred  feet  long,  and  not  ex- 
ceeding one  hundred  and  fifty  long,  into  ten  equal  parts. 

Class  4.  Vessels  of  which  the  tonnage  length  according  to  the  above 
measurement  is  above  one  hundred  and  fifty  feet,  and  not 
exceeding  two  hundred  feet  long,  into  twelve  equal  parts. 

Class  5.  Vessels  of  which  the  tonnage  length  according  to  the  above 
measurement  is  above  two  hundred  feet,  and  not  exceeding 
two  hundred  and  fifty  feet  long,  into  fourteen  equal  parts. 

Class  6.  Vessels  of  which  the  tonnage  length  according  to  the  above 
measurement  is  above  two  hundred  and  fifty  feet  long,  into 
sixteen  equal  parts. 

METHOD  OF  FINDING  THE  AREAS. 

Transverse  Areas. — Then,  the  hold  being  sufficiently 
cleared  to  admit  of  the  required  depths  and  breadths  being 
properly  taken,  find  the  transverse  area  of  such  vessel  at 
si  2* 


18 


AN    ACT    TO    REGULATE   THE 


each  point  of  division  of  the  length  as  follows  : — Measure 
the  depth  at  each  point  of  division  from  a  point  at  a  dis- 
tance of  one-third  of  the  round  of  the  beam  below  such 
deck,  or,  in  case  of  a  break,  below  a  line  stretched  in 
continuation  thereof,  to  the  upper  side  of  the  floor-timber, 
at  the  inside  of  the  limber-strake,  after  deducting  the 
average  thickness  of  the  ceiling,  which  is  between  the 
bilge-planks  and  limber-strake ;  then,  if  the  depth  at  the 
midship  division  of  the  length  do  not  exceed  sixteen  feet, 
divide  each  depth  into  four  equal  parts  ;  then  measure  the 
inside  horizontal  breadth,  at  each  of  the  three  points  of 
division,  and  also  at  the  upper  and  lower  points  of  the 
depth,  extending  each  measurement  to  the  average 
thickness  of  that  part  of  the  ceiling  which  is  between  the 
points  of  measurement ;  number  these  breadths  from 
above,  (numbering  the  upper  breadth  one,  and  so  on 
down  to  the  lowest  breadth  ;)  multiply  the  second  and 
fourth  by  four,  and  the  third  by  two  ;  add  these  products 
together,  and  to  the  sum  add  the  first  breadth  and  the 
last,  or  fifth ;  multiply  the  quantity  thus  obtained  by  one- 
third  of  the  common  interval  between  the  breadths, 
and  the  product  shall  be  deemed  the  transverse  area  ; 
but  if  the  midship  depth  exceed  sixteen  feet,  divide  each 
depth  into  six  equal  parts,  instead  of  four,  and  measure, 
as  before  directed,  the  horizontal  breadths  at  the  five 
points  of  division,  and  also  at  the  upper  and  lower  points 
of  the  depth ;  number  them  from  above  as  before  ;  mul- 
tiply the  second,  fourth,  and  sixth  by  four,  and  the  third 
and  fifth  by  two ;  add  these  products  together,  and  to  the 
sum  add  the  first  breadth  and  the  last,  or  seventh  ;  mul- 
tiply the  quantities  thus  obtained  by  one- third  of  the 
common  interval  between  the  breadths,  and  the  product 
shall  be  deemed  the  transverse  area. 


ADMEASUREMENT  OF  TONNAGE.  19 

METHOD  OF  ASCERTAINING  THE  REGISTER  TONNAGE  OF  VESSEL. 

Computation  from  Areas. — Having  thus  ascertained  the 
transverse  area  at  each  point  of  division  of  the  length  of 
the  vessel,  as  required  above,  proceed  to  ascertain  the  reg- 
ister tonnage  of  the  vessel  in  the  following  manner : — 
Number  the  areas  successively  one,  two,  three,  <fcc.,  num- 
ber one  being  at  the  extreme  limit  of  the  length  at  the 
bow,  and  the  last  number  at  the  extreme  limit  of  the  length 
at  the  stern ;  then  whether  the  length  be  divided  ac- 
cording to  table,  into  six  or  sixteen  parts,  as  in  classes 
one  and  six,  or  any  intermediate  number,  as  in  classes 
two,  three,  four,  and  five,  multiply  the  second,  and  every 
even  numbered  area,  by  four,  and  the  third  and  every 
odd  nitmbered  area  (except  the  first  and  last)  by  tu-o  ; 
add  these  products  together,  and  to  the  sum  add  the  first 
and  last,  if  they  yield  anything  ;  multiply  the  quantities 
thus  obtained  by  one-third  of  the  common  interval  be- 
tween the  areas,  and  the  product  will  be  the  cubical  con- 
tents of  the  space  under  the  tonnage-deck  ;  divide  this 
product  by  one  hundred,  and  the  quotient,  being  the  ton- 
nage under  the  tonnage-deck,  shall  be  deemed  to  be  the 
register  tonnage  of  the  vessel,  subject  to  the  additions 
hereinafter  mentioned. 

MEASUREMENT  OF  THE  POOP  AND  OTHER  CLOSED  IN  SPACE. 

If  there  be  a  break,  a  poop,  or  any  other  permanent, 
closed-in  space  on  the  upper  decks,  on  the  spar  deck, 
available  for  cargo,  or  stores,  or  for  the  berthing  or  accom- 
modation of  passengers  or  crew,  the  tonnage  of  such  space 
shall  be  ascertained  as  follows : — 

Measure  the  internal  mean  length  of  such  space  in 
feet,  and  divide  it  into  an  even  number  of  equal  parts 


20  AN  ACT   TO   REGULATE    THE 

of  which  the  distance  asunder  shall  be  most  nearly 
equal  to  those  into  which  the  length  of  the  tonnage-deck 
has  been  divided  ;  measure  at  the  middle  of  its  height 
the  inside  breadths,  namely,  one  at  each  end  and  at 
each  of  the  points  of  division,  numbering  them  succes- 
sively, one,  two,  three,  &c. ;  then  to  the  sum  of  the  end 
breadths  add  four  times  the  sum  of  the  even-numbered 
breadths  and  twice  the  sum  of  the  odd-numbered  breadths,' 
except  the  first  and  last,  and  multiply  the  whole  sum  by 
one-third  of  the  common  interval  between  the  breadths  ; 
the  product  will  give  the  mean  horizontal  area  of  such 
space ;  then  measure  the  mean  height  between  the  planks 
of  the  decks,  and  multiply  by  it  the  mean  horizontal  area ; 
divide  the  product  by  one  hundred,  and  the  quotient  shall 
be  deemed  to  be  the  tonnage  of  such  space,  and  shall  be 
added  to  the  tonnage  under  the  tonnage-decks,  ascertained 
as  aforesaid. 

MEASUREMENT  OF  THE  THIRD  OR  SPAR  DECK. 

If  a  vessel  has  a  third  deck,  or  spar-deck,  the  tonnage 
of  the  space  between  it  and  the  tonnage-deck  shall  be 
ascertained  as  follows: — 

Measure  in  feet  the  inside  length  of  the  space,  at  the 
middle  of  its  height,  from  the  plank  at  the  side  of  the 
stem,  to  the  plank  on  the  timbers  at  the  stern,  and  di- 
vide the  length  into  the  same  number  of  equal  parts  into 
which  the  length  of  the  tonnage-deck  is  divided  ;  measure 
(also  at  the  middle  of  its  height)  the  inside  breadth  of  the 
space  at  each  of  the  points  of  division,  also  the  breadth 
of  the  stem  and  the  breadth  at  the  stem  ;  number  them 
successively,  one,  two,  three,  &c.,  commencing  at  the 
stem:  multiply  the  second,  and  all  other  even  num- 
bered breadths,  by  four,  and  the  third,  and  all  the  other 


ADMEASUREMENT    OF    TONNAGE.  21 

odd  numbered  breadths,  (except  the  first  and  last,)  by 
two  ;  to  the  sum  of  these  products  add  the  first  and  last 
breadths,  multiply  the  whole  sum  by  one-third  of  the 
common  interval  between  the  breadths,  and  the  result 
will  give,  in  superficial  feet,  the  mean  horizontal  area  of 
such  space  ;  measure  the  mean  height  between  the  plank 
of  the  two  decks,  and  multiply  by  it  the  mean  horizontal 
area,  and  the  product  will  be  the  cubical  contents  of  the 
space;  divide  this  product  by  one  hundred,  and  the  quo- 
tient shall  be  deemed  to  be  the  tonnage  of  such  space, 
and  shall  be  added  to  the  other  tonnage  of  the  vessel, 
ascertained  as  aforesaid.  And  if  the  vessel  has  more 
than  three  decks,  the  tonnage  of  each  space  between 
decks,  above  the  tonnage-deck,  shall  be  severally  ascer- 
tained in  the  manner  above  described,  and  shall  be  added 
to  the  tonnage  of  the  vessel,  ascertained  as  aforesaid. 

TONNAGE  OF  OPEN  VESSELS  HOW  ASCERTAINED. 
In  ascertaining  the  tonnage  of  open  vessels  the  upper 
edge  of  the  upper  strake  is  to  form  the  boundary  line  of 
measurement,  and  the  depth  shall  be  taken  from  an 
athwartship  line,  extending  from  upper  edge  of  said 
strake  at  each  division  of  the  length. 

REGISTERED  TONNAGE  TO  BE  CARVED  ON  THE  MAIN  BEAM. 

The  register  of  the  vessel  shall  express  the  number 
of  decks,  the  tonnage  under  the  tonnage-deck,  that  of 
the  between-decks,  above  the  tonnage  deck ;  also  that 
of  the  poop  or  other  enclosed  spaces  above  the  deck, 
each  separately.  In  every  registered  United  States  ship 
or  -vessel  the  number  denoting  the  total  registered  ton- 
nage shall  be  deeply  carved  or  otherwise  permanently 
marked  on  her  main  beam,  and  shall  be  so  continued ; 


22  ADMEASUREMENT   OF   TONNAGE. 

and  if  it  at  any  time  cease  to  be  so  continued,  such  ves- 
sel shall  no  longer  be  recognized  as  a  registered  United 
States  vessel. 

CHARGE  FOR  MEASURING  AND  CERTIFICATE, 

SEC.  4.  And  be  it  further  enacted,  That  the  charge  for 
the  measurement  of  tonnage  and  certifying  the  same 
shall  not  exceed  the  sum  of  one  dollar  and  fifty  cents  for 
each  transverse  section  under  the  tonnage-deck ;  and  the 
sum  of  three  dollars  for  measuring  each  between-decks 
above  tlie  tonnage-deck  ;  and  the  sum  of  one  dollar  and 
fifty  cents  for  each  poop,  or  closed-in  space  available  for 
cargo  or  stores,  or  for  the  berthing  or  accommodation  of 
passengers,  or  officers  and  crew  above  the  upper  or  spar- 
deck. 

ACT  NOT  TO  APPLY   TO  VESSELS    NOT   REQUIRED   TO    BE   REGIS- 
TERED OR  ENROLLED. 

SEC.  5.  And  be  it  further  enacted,  That  the  provisions 
of  this  act  shall  not  be  deemed  to  apply  to  any  vessel 
not  required  by  law  to  be  registered,  or  enrolled,  or  li- 
censed, and  all  acts  and  parts  of  acts  inconsistent  with 
the  provisions  of  this  are  hereby  repealed. 

ApppovedMaij  6,  1864. 


SUPPLEMENT. 


ACT  OF  CONGRESS  AMENDATORY  OF  THE  ACT  OF  1864, 
Approved,  February  28,   1865. 

Be  it  enacted,  fyc.,  That  the  act  entitled  "  An  act  to 
regulate  the  admeasurement  of  tonnage  of  ships  and 
vessels  of  the  United  States,"  approved  May  sixth, 
eighteen  hundred  and  sixty-four,  shall  be  so  construed 
that  no  part  of  any  ship  or  vessel  shall  be  admeasured 
or  registered  for  tonnage  that  is  used  for  cabins  or  state- 
rooms, and  constructed  entirely  above  the  first  deck, 
which  is  not  a  deck  to  the  hull. 


ANALYSIS    OF    THE   MODE 

FOR   THE 

ADMEASUREMENT    OF    TONNAGE. 


The  following  "MODE"  for  the  Admeasurement  of  Vessels,  with 
Examples  of  its  application  to  the  purposes  of  Naval  Architecture, 
&c.,  have  been  taken  from  the  **  Review  of  the  Laws  of  Tonnage,'* 
by  G.  Moorsom,  London.  —  This  MODE  for  Measuring  Vessels  was 

.  adopted  by  the  British  Government,  by  Act  of  Parliament,  in  1854, 
which  Act  has  been  substantially  copied  into  the  "  Act  to  regulate 
the  Admeasurement  of  Ships  and  Vessels  of  the  United  States," 
Approved,  May,  1864.  The  Formulae  in  *'  Moorsom's  Review," 
have  been  altered  to  conform  to  the  Table  of  Classes'in  the  United 
States  Law.* 


PLAN    BASED    ON    INTERNAL    CAPACITY. 

The  system,  for  the  admeasurement  of  vessels  when  the  hold 
is  clear,  consists  of  a  series  of  internal  measurements,  which  at 
the  time  of  taking  them,  are  simply  arranged  in  a  prepared  form- 
ula, from  which  the  true  cubical  contents,  and  thence  the  ton- 
nage, are  directly  computed  by  an  easy  arithmetical  process. 

The  plan  is  founded  or  based  on  the  correct  internal  capacity  of 
vessels.  The  first  object,  therefore,  was  to  attain  a  practically 
correct  cubature  of  this  space.  This  is  accomplished  by  means 

*  The  United  States  Rule  of  Measurement  for  vessels  is  similar  to 
that  of  the  English  law,  the  principal  difference  being  that  ours  has  a 
greater  number  of  areas  or  sections  ;  making  it  more  accurate  and 
nearer  the  true  internal  capacity  of  the  vessel. 

The  following  is  the  English  Table  of  areas  or  sections  :  — 
Vessels  of  which  the  tonnage  length  is 

50  ft.  or  under  -----  into  4  equal  parts, 
above  50  ft.  and  not  exceeding  120  ft.  into  6  equal  parts, 
above  120  ft.  and  not  exceeding  180  ft.  into  8  equal  parts, 
above  180  ft.  and  not  exceeding  225  ft.  into  10  equal  parts, 
above  225  ft.  -  - into  12  equal  parts. 


24          ANALYSIS  OF  THE  MODE  FOR  THE 

purely  legitimate  ;  and  the  number  of  cubic  feet  so  arrived  at  is 
divided  by  100  for  the  register  tonnage. 

From  this  brief  definition  of  the  plan  it  is  obvious  that  the 
tonnage  resulting  from  it  must  afford  an  immediate  and  just 
knowledge  of  the  capacities  or  sizes  of  all  vessels,  whatever  be 
their  form. 

The  tonnage  so  ascertained  is  simply  a  cubical  tonnage  or  true 
expression  of  the  internal  cubical  capacity,  in  which  every  ton  of 
tonnage  represents  100  cubic  feet  of  space.  So  that,  if  by  this 
process  one  vessel  measures  500  tons,  for  instance,  and  another 
measures  1000  tons,  it  is  known  to  a  certainty  that  the  latter  ves- 
sel has  double  the  cubical  capacity  of  the  former  ;  for,  in  each  case, 
every  ton  of  tonnage  contains  exactly  100  cubic  feet  of  space. 

Or,  speaking  generally  of  the  size  of  these  two  vessels,  we 
should  say  of  the  first,  that  she  is  a  vessel  of  500  tons  cubical 
measurement,  of  100  cubic  feet  to  the  ton  ;  and  of  the  sec- 
ond, that  she  is  a  vessel  of  1000  tons  cubical  measurement,  of 
100  cubic  feet  to  the  ton :  having  thereby  a  clear  knowledge  not 
only  of  the  comparative  magnitudes  of  the  two,  but  of  the  real  cu- 
bical capacity  of  each. 

External  measurement,  even  when  applied  to  ascertaining  the 
weight  of  the  actual  cargo  of  vessels,  is  not  an  eligible  standard 
for  tonnage  admeasurement,  inasmuch  as  heavy  or  dead-weight 
cargoes  are  not  the  predominant  cargoes  of  commerce. 

And  that,  when  applied  to  any  other  extent,  it  is  totally  inad- 
missible ;  inasmuch  as  it  is,  then,  neither  a  measure  of  the  weight 
of  cargoes,  nor  of  the  internal  capacity  :  while,  at  the  same  time, 
it  is  productive  of  various  inequalities  operating  most  unjustly 
to  (the  advantage  of  iron  built  vessels  ;  being  an  inducement, 
moreover,  to  the  building  of  weak,  thin-sided  vessels. 

While,  on  the  contrary,  internal  measurement,  being  a  meas- 
ure of  the  internal  capacity,  identified  with  the  prevailing  car- 
goes of  commerce,  is  a  fair  and  eligible  basis  for  all  the  purposes 
for  which  tonnage  admeasurement  is  established,  as  well  for  ves- 
sels built  of  iron  as  those  built  of  wood  ;  having  an  equalizing 
effect  with  regard  to  wood  and  iron  vessels,  and  being  at  the  same 
time,  unattended  by  any  inequalities  in  its  operation,  except  giv- 
ing an  advantage  in  cases  of  heavy  cargoes  carried  by  vessels  of 
increased  scantlings;  which,  being  few  in  comparison,  argue 
little  in  opposition  to  its  general  eligibility ;  more  particularly 
when  it  is  considered  that  this  very  disadvantage  is,  in  itself,  an 
encouragement  to  the  building  of  strong,  thick-sided  vessels,  the 
opposite  of  which  is  the  tendency  of  external  measurement. 


ADMEASUREMENT  OF  TONNAGE.  25 

RULE  FOR  DETERMINING  THE  REGISTER 
TONNAGE. 

Outline  of  Mode. 

In  all  vessels,  except  those  haying  a  spar  or  third  deck,  the 
upper  deck  is  the  tonnage-deck,  that  is,  the  deck  from  which  the 
tonnage  of  the  hold  is  computed  ;  but  in  vessels  having  a  spar 
or  third  deck,  the  middle  deck  is  the  tonnage-deck  ;  and  the  ton- 
nage of  the  spaces  above  the  tonnage-deck  is  in  each  case  com- 
puted separately. 

The  inside  length  of  the  vessel  at  the  medium  height  of  the 
tonnage-deck  is  divided  into  a  given  number  of  equal. parts,  ac- 
cording to  the  length  of  the  vessel ;  at  each  of  the  points  of  di- 
vision a  perpendicular  transverse  area  of  the  vessel  is  calculated, 
by  means  of  a  general  process  hereinafter  described  ;  and  from 
these  areas  (by  means  of  the  same  general  process  as  the  areas 
themselves  are  calculated)  the  cubical  content  under  the  deck  is 
ascertained  ;  this  cubical  content  is  then  divided  by  100,  which 
gives  the  register  tonnage  under  the  deck. 

This  is  an  outline  of  the  operation  ;  from  which  it  will  be  seen 
that,  when  only  the  general  process  of  obtaining  the  areas  is  un- 
derstood, the  whole  theory  of  the  system  is  substantially  known. 


GENERAL  PROCESS  FOR  FINDING  AN  AREA,  &c. 
ART.  1. — First,  as  to  the  means  by  which  the  areas  are  obtained: — 
The  depth  of  the  vessel  is  taken  at  the  area  to  be  measured,  and 
being  divided  into  a  certain  number  of  equal  parts,  the  horizontal 
breadths  (required  to  be  always  odd  in  their  number)  are  meas- 
ured at  each  point  of  division,  also  at  the  top  and  bottom  of  the 
depth ;  these  breadths  are  then  numbered  in  consecutive  order, 
and  placed  accordingly  in  the  general  formula  which  follows. 
The  even  numbered  breadths,  as  2,  4,  &e.,  are  then  multiplied  by 
4,  and  the  odd  numbered  ones  (except  the  first  and  last),  as  3,  5, 
&c.,  are  multiplied  by  2  ;  and  the  sum  of  these  products,  added 
to  the  first  and  last  breadths,  is  then  multiplied  by  one-third  of 
the  common  interval  between  the  breadths,  which  gives  the  area 
contained  between  the  top  and  bottom  breadths,  as  required. 

Example  of  the  Measurement  of  an  Area. 
Supposing  the  depth  of  the  area  to  be  twelve  feet,  and  to  be 
divided  into  four  equal  parts,  the  common  interval  between  the 

Bl  3 


^6         ANALYSIS  OF  THE  MODE  FOR  THE 

breadths  is  three  feet,  so  that  one-third  of  the  common  interval  is 
one  foot;  and  supposing  the  breadths  to  be  4,  8,  12,  16  and  20 
feet  as  shown  in  the  figure  below,  the  process  is  as  follows : — 

20  feet  breadth, 


GENERAL  FORMULA. 

Depth  12  ft.  -f-  4  =  3  ft.  the 
com.  int.  beta,  breadths. 

No. 

Multi- 
pliers. 

Breadths. 

Products. 

1 

1 

20 

20 

2 

4 

16 

64 

3 

2 

12 

24 

4 

4 

8 

32 

5 

1 

4 

4 

144 

1  is  &  of  com.  int.  betn.  breadths. 

144  area  required. 
In  the  same  manner  each  area  is  obtained. 


ADMEASUREMENT   OF  TONNAGE.  27 

THE  CUBICAL  CONTENT  UNDER  THE  TONNAGE-DECK. 

ART.  2. —  The  cubical  content  under  the  tonnage-deck  is  obtained 
by  means  of  the  same  general  process ,  applied  to  the  areas  above 
found,  as  follows : — 

The  areas  are  numbered  in  consecutive  order,  commencing  at 
the  bow,  as  shown  in  the  figure  annexed.  The  first  area  at  the 
extreme  limit  of  the  bow  is  easily  conceived,  by  inspection  of  the 
figure,  to  vanish  into  a  line  the  breadth  of  the  stem,  and  is  there- 
fore equal  to  0  ;  and  the  last  area  at  the  extreme  limit  of  the  stern 
vanishes,  in  a  similar  manner,  into  a  line  the  breadth  of  the  stern, 
and  is  therefore  also  equal  to  0.  But  although  these  terminal 
areas  are  here  equal  to  0,  they  are,  nevertheless,  to  act  their  parts 
in  the  formula  just  in  the  same  manner  as  the  terminal  breadths 
do,  in  the  case  of  the  areas.  This  being  understood,  the  process 
of  obtaining  the  cubical  contents  from  the  areas  is  exactly  the 
same  as  that  of  obtaining  the  areas  from  the  breadths ;  that  is  to 
say  (having  numbered  the  areas  in  consecutive  order,  beginning 
at  the  bow),  the  even  numbered  ones,  as  2,  4,  &c.,  are  multi- 
plied by  4,  and  the  odd  numbered  ones  (except  the  first  and  last), 
as  3,  5,  &c.,  are  multiplied  by  2  ;  and  the  sum  of  these  products, 
added  to  the  first  and  last  areas,  is  then  multiplied  by  one-third 
of  the  common  interval  between  the  areas,  which  gives  the  cubi- 
cal content  required. 

Example  of  computing  the  Cubical  Content  below  the  Tonnage-deck 
by  means  of  the  Transverse  Areas. 

Supposing  the  inside  length  of  the  vessel,  at  the  tonnage  or 
upper  deck,  as  prescribed  to  be  taken,  to  be  96  feet,  it  is  divided 
into  eight  equal  parts  ;  this  gives  seven  points  of  division  or  areas, 
in  addition  to  the  terminal  ones  at  the  extreme  limits  of  the  bow 
and  stern,  as  seen  by  inspection  of  the  figure  below  ;  and  the  com- 
mon interval  between  the  areas  being  12  feet,  one-third  of  the 
common  interval  is  four  feet. 

And  supposing  the  areas,  found  as  in  the  foregoing  example, 
to  be  as  set  forth  at  the  points  of  division  in  the  figure,  the  pro- 
cess is  as  follows  : — 

No.7.  No.  6.  No.  5.  No.  4.  No.  3.  No.  2.  No.  1, 
Area  Area  Area  Area  Area  Area  Area 
120  130  144  144  130  125 

Tonnage  or  upper  Deck.  ?\f 


r 


28 


ANALYSIS  OF  THE  MODE  FOR  THE 


GENERAL  FORMULA. 

Length  96  ft.  -r-  8  =  12  ft.  the 
com.  int.  betn.  areas. 

No. 

Multi- 
pliers. 

Areas. 

Products. 

1 

1 

0 

0 

2 

4 

125 

500 

3 

2 

130 

260 

4 

4 

144 

576 

5 

2, 

144 

288 

6 

4 

130 

520 

7 

2 

120 

240 

8 

4 

105 

420 

9 

1 

0 

0 

2804 


4  is  &  of  12  com.  int.  between  the  areas. 


11216  cubic  content  under  deck. 

Hence  we  see  the  identity  in  the  two  operations,  of  finding  the 
areas,  and  the  cubical  content  under  the  deck  from  them ;  which, 
as  already  observed,  constitutes  the  whole  theory  of  the  plan. 

Tha  cubical  content  having  been  thus  found,  it  is  to  be  divided 
by  100  for  the  register  tonnage,  that  is, 

Cub.  Ft.  Tons 

11216  -H  100  =  112.16  register  tonnage  under  the  deck. 


CORRECTNESS   or  PROCESS  PROVED  BY  EXAMPLES. 

ART.  3. — The  general  process  having  been  thus  delineated,  it 
may  be  desirable  next  to  show  how  far  it  can  be  depended  upon, 
as  to  the  correctness  of  the  results  derived  from  it. 

For  this  purpose  the  following  examples  are  introduced  ;  first 
premising,  that  notwithstanding  the  simplicity  of  the  operation, 
it  is,  nevertheless,  founded  on  the  purest  mathematical  principles. 


ADMEASUREMENT    OP    TONNAGE. 


29 


The  four  following  examples  are  selected  as  comprising  within 
their  limits  the  most  extreme  forms  which  merchant  ships  can 
possibly  partake  of,  from  the  fullest  flat-bottomed  coaster  to  the 
sharpest  wedge-like  fruit-vessel ;  and  as  they  are  known  regular 
figures  of  easy  quadrature,  namely,  the  parallelogram,  circle,  par- 
abola, and  triangle,  they  afford  the  means  of  geometrical  com- 
parison, by  which  the  correctness  of  the  Rule  can  be  exactly 
estimated. 


EXAMPLE  1. 
Parallelogrammical  or  Wall- sided  Form. 

Suppose  the  upper  breadth,  or  breadth  at  tonnage-deck,  to  be 
20  feet,  and  the  depth  12  feet. 

The  depth  being  divided  into  four  equal  parts,  the  common  in- 
terval between  the  breadths  is  three  feet,  so  that  one-third  of  the 
common  interval  is  one  foot.  And  the  several  breadths,  from 
the  nature  of  the  figure,  being  equal  to  each  other,  the  process  is 
as  follows : — 

Measurement  by  TONNAGE  RULE. 


GENERAL  FORMULA. 

Depth  12  ft.  -*•  4  =  3  ft.  the 
com.  int.  betn.  breadths. 

No. 

Multi 
pliers. 

Breadths. 

Products. 

1 

1 

20 

20 

2 

4 

20 

80 

3 

2 

20 

40 

4 

4 

20 

80 

5 

1 

20 

20 

240 


1  is  J  of  3,  com.  int.  between  breadths. 


Bl 


sq.  ft.  240  area  required. 
3* 


30 


ANALYSIS    OF   THE   B10DE    FOR   THE 


EXAMPLE  2. 
Circular  Form. 

Suppose  the  upper  breadth  to  be  20  feet,  and  the  depth,  in  this 
case,  to  be  10  feet,  so  that  the  area  may  be  a  perfect  semicircle. 

The  depth  being  divided  into  four  equal  parts,  the  common  in- 
terval between  the  breadths  is,  in  this  case,  2.5  feet,  so  that  one- 
third  of  the  common  interval  is  .833  feet.  And  the  several 
breadths,  measured  from  the  figure,  being  as  shown  in  the  form- 
ula, the  process  is  as  follows  ; — 


Measurement  by  TONNAGE   RULE. 


*• 

o' 

GENERAL  FORMULA. 

rH 

Depth  10  ft.  -f-  4  =2.5  ft.  the 
com.  int.  betn.  breadths. 

?9» 
•h 

rH 
CO 

X 

"w 

f 

1 

No. 

Multi 
pliers. 

Breadths. 

Products. 

3 

?* 

S-t 
II 

1 

1 

20 

20 

*cs 

t-A 

1 

Si 

•J 

2 

4 

19.5 

78 

1 

"g 

1* 

K 

3 

2 

17.5 

35 

i 

e3 

4 

4 

13.5 

54 

i 

d 

5 

1 

0 

0 

11 


X       .  1  g 

g  1;l 


^  15 
cr1  M 

2  £ 


o<  •-  a 

.2      «a|- 

H    R'lr 

^    <=>  |S< 

EH        *-   ^  esc 


187 
.833  is  J  of  2.5  com.  int.  between  breadths. 


sq.  ft.  155.771  area  required. 


ADMEASUREMENT     OF    TONNAGE. 


31 


EXAMPLE  3. 
Parabolic  Form. 

Suppose  the  upper  breadth  to  be  20  feet,  and  the  depth  12  feet. 
Then  the  focus  of  the  parabola  from  vertex  is  3.6  feet.     And 
the  principal  parameter  is  14.4  feet,  from  which  elements  the 
figure  is  geometrically  constructed. 

The  depth  being  divided  into  four  equal  parts,  the  common  in- 
terval between  the  breadths  is  three  feet,  so  that  one-third  of  the 
common  interval  is  one  foot.  And  the  several  breadths,  measured 
from  the  figure,  being  as  shown  in  the  formula,  the  process  is  as 
follows  :— 

Measurement  by  TONNAGE    RULE. 


GENERAL  FORMULA. 

Depth  12  ft.  -^  4  =3  ft.  the 
com.  int.  betn.  breadths. 

No. 

Multi- 
pliers. 

Breadths. 

Products. 

1 

1 

20 

20 

2 

4 

18.8 

76.2 

3 

2 

15.2 

30.4 

4 

4 

8.6 

34.4 

6 

1 

0 

0 

»  x  •§ 


160 


1  is  £  of  3  com.  int.  between  breadths, 
sq.  ft,  160  area  required. 


EXAMPLE  4. 
Triangular  or  Wedge-like  Form. 

Suppose,  again,  the  upper  breadth  to  be  20  feet,  and  the  depth 
12  feet. 
The  depth  being  divided  into  four  equal  parts,  the  common  in- 


32 


ANALYSIS  OF  THE  MODE  FOR  THE 


terval  between  the  breadths  is  three  feet,  so  that  one-third  of  the 
common  interval  is  one  foot. 

And  the  several  breadths,  being  as  shown  in  the  formula,  the 
process  is  as  follows  : — 

Measurement  by  TONNAGE   RULE. 


GENERAL  FORMULA. 

Depth  12  ft.  -f-  4  =  3  ft.  the 
com.  int.  betn.  breadths. 

No. 

Multi- 
pliers. 

Breadths. 

Products. 

1 

1 

20 

20 

2 

4 

16 

60 

3 

2 

10 

20 

4 

4 

5 

20 

5 

1 

0 

0 

120 
lis£ 

of  3,  com.  int.  between  breadths. 

sq.  ft.  120  area  required. 

Having  thus  shown  that  the  process,  when  applied  to  the  fullest 
and  sharpest,  as  well  as  to  the  intermediate  shapes  of  the  circle 
and  parabola,  may  be  considered,  in  a  practical  sense,  as  being 
mathematically  correct,  it  may  be  fairly  inferred  that  its  opera- 
tions, in  all  other  cases  conceivable  to  lie  between  these  extremes, 
will  be  attended  with  equally  satisfactory  results  ;  at  the  same 
time  observing  that  the  greater  the  irregularity  of  the  curve,  or 
in  the  deviations  of  the  breadths,  the  greater  should  be  the  num- 
ber (always  an  odd  number)  of  breadths  employed. 

In  the  four  preceding  examples,  the  investigation  of  the  meas- 
urement of  areas  only  has  been  the  question.  But  the  process  is 
equally  valuable  for  ascertaining  the  cubature  of  solids.  The 
rationale  of  its  equal  eligibility  in  the  one  case  as  in  the  other  is 
easily  conceived,  as  follows : — 

A  circumscribed  area  can  be  supposed  to  be  completely  cov- 
ered by  an  infinite  number  of  lines  or  breadths  indefinitely  near 


ADMEASUREMENT     OF    TONNAGE.  33 

to  each  other ;  and  as  these  breadths  wholly  make  up  the  area,  it 
is  manifest  that  the  sum  of  them  must  be  the  area  itself.  Now 
the  integration  of  these  breadths  is  exactly  what  the  rule  effects, 
by  the  employment,  as  already  shown,  of  only  a  few  of  them. 

In  the  same  manner,  if  we  conceive  a  solid  body  to  be  made 
up  of  an  infinite  number  of  sections  or  areas  indefinitely  near  to 
each  other,  it  is  manifest  that  the  sum  of  these  areas  or  infinitesi- 
mal laminae  constitute  the  body  itself. 

As  the  process  must  equally  accomplish  the  summation  of  the 
areas  as  it  does  that  of  the  breadths,  ifVe  substitute  the  areas  for 
the  breadths,  it  must  therefore  be  equally  applicable  to  the  cuba- 
ture  of  solids  as  it  is  to  the  measurement  of  areas.  (See  page  65.) 


TONNAGE   OF  THE  SPACES  ABOVE  DECK. 

ART.  4. — The  method  of  obtaining  the  tonnage  under  the  ton- 
nage deck,  having  now  been,  generally,  described,  the  tonnage 
of  the  spaces  above  this  deck,  (videlicet  the  poop,  forecastle,  &c. , 
and  in  ships  having  a  third  or  spar-deck,  the  space  between  the 
spar  and  tonnage-decks,)  being  ascertained  on  the  same  principles, 
a  practical  example  of  each  will  be  readily  understood. 

MEASUREMENT    OF    THE    POOP. 

The  inside  length  of  the  poop,  at  the  middle  of  its  height,  is 
first  taken,  and  divided  into  two  equal  parts  ;*  three  breadths  (also 
at  the  middle  of  its  height)  are  then  measured  (numbered  in  the 
formula  1,  2,  3),  the  first  at  the  fore  end  of  the  poop,  tlie  second 
at  the  middle  point  of  its  length,  and  the  last  at  its  after  end  ; 
then  to  the  first  and  last  of  these  breadths  add  four  times  the  mid- 
dle one,  and  multiply  the  sum  by  one-third  of  the  common  inter- 
val between  them,  which  gives  a  mean  horizontal  area  of  the 
poop ;  this,  being  multiplied  by  its  height,  gives  its  cubical  content, 
which,  divided  by  one  hundred,  gives  the  tonnage  of  the  poop. 

Example  of  Computation. 

Suppose  the  inside  length  at  the  middle  of  the  height  to  be 
sixty  feet ;  this,  being  divided  into  two  equal  parts,*  gives  thirty 
feet  for  the  common  interval  between  the  breadths,  so  that  one- 
third  of  the  common  interval  is  ten  feet. 

Suppose,  also,  the  height  of  the  poop  to  be  six  feet,  and  the 
three  breadths,  measured  as  above  directed,  to  be  as  set  forth  in 
the  following  formula,  the  process  is  then  as  follows  : — 

NOTE.  *  The  United  States  Rule  for  measuring  the  Poop  or  any  other  perma- 
nent closed-in  space  on  the  upper  deck,  available  for  cargo,  stores,  &c.,  requires 
that  it  shall  be  divided  into  an  even  number  of  equal  parts,  of  which  the  distance 
asunder  shall  be  most  nearly  equal  to  those  inlo  which  the  length  of  the  tonnage- 
deck  has  been  divided.  [See  Law  at  page  19.] 


ANALYSIS    OF   THE   MODE   FOR   THE 


GENERAL  FORMULA. 

Length  60  ft.  -j-  2  =  30  ft.  the 
com.  int.  betn.  breadths.* 

No. 

Multi- 
pliers. 

Breadths. 

Products. 

1 

1 

20 

20 

2 

4 

19 

76 

3 

1 

18 

18 

114 
10  is  J 

of  30,  com.  int.  between  breadths, 
sq.  ft.  1140  mean  horizontal  area  of  poop. 
6  height. 

Cubic  content  6840  -f- 100  =  68.4  tons,  reg.  ton.  of  poop. 

It  will  be  seen  that  the  above  formula  is  the  same  as  that  em- 
ployed in  the  examples  of  finding  the  areas  in  the  preceding  Ar- 
ticles 1  and  3,  with  this  difference,  only,  that  fewer  ordinates 
or  breadths  are  here  employed.  If  five  or  seven  breadths  are 
measured  instead  of  three,  then  the  odd  numbered  breadths  (ex- 
cluding the  first  and  last)  must  be  multiplied  by  two,  as  in  those 
examples. 


*  See  Note  on  precedin 
ates  Rule  for 
the  upper  deck. 


page,  and  Law  at  page  19,  for  United 
States  Rule  for  measuring  tlie  Poop  or  other  closed-in  Space  on 


MEASUREMENT    OF    THE    FORECASTLE. 

The  admeasurement  of  the  forecastle  is  precisely  the  same  as 
that  for  the  poop,  No.  1  at  the  fore  end  of  the  forecastle,  being 
the  breadth  of  the  stem  at  that  place,  &c. 

Example  of  Computation. 

Suppose  the  inside  length  at  the  middle  of  its  height  to  be  thirty 
feet  ;  this,  being  divided  into  two  equal  parts,  gives  fifteen  feet  for 
the  common  interval  between  the  breadths,  so  that  one-third  of 
the  common  interval  is  five  feet. 

Suppose,  also,  the  height  of  the  forecastle  to  be  six  feet,  and 
the  three  breadths,  measured  as  above  directed,  to  be  as  set  forth 
in  the  following  formula,  the  process  is  then  as  follows  :  — 


ADMEASUREMENT     OF    TONNAGE. 


35 


GENERAL  FORMULA. 

Length  30  ft.  -r-  2  =  15  ft.  the 
com.  int.  betn.  breadths. 

No. 

Multi- 
pliers. 

Breadths. 

Products. 

1 

1 

1.25 

1.25 

2 

4 

14.00 

56.00 

3 

1 

20.00 

20.00 

77.25 

5  is  J  of  15,  com.  int.  between  breadths. 


• .  25  mean  horizontal  area  of  forecastle. 
6  height  of  forecastle. 


Cubic  content  2317. 50 


100  =  23.17  tons,  register  tonnage 
of  forecastle. 


SPAR  AND  TONNAGE-DECKS. 

Measurement  of  the  Space  between  the  Spar  and  Tonnage-Decks  in 
Vessels  having  a  Spar  or  Third  Deck. 

Here,  also,  the  process,  except  in  the  nature  of  the  details,  is 
identically  the  same  as  in  all  the  preceding  cases. 

The  inside  length  of  this  space,  at  the  middle  of  its  height,  is 
first  taken,  and  divided  into  the  same  number  of  equal  parts  as 
there  are  divisions  of  the  length  of  the  tonnage-deck  ;  the  inside 
breadths  (also  at  the  middle  of  its  height),  at  each  of  the  points 
of  division,  are  then  measured,  also  the  breadth  at  the  stern  and 
the  breadth  of  the  stem;  and  numbering  them  successively  1,  2, 
3,  &c.,  (No.  1  being  that  of  the  stem),  multiply  the  2nd,  4th, 
6th,  &c.,  including  all  the  even  numbered  breadths,  by  4,  and  the 
3rd,  5th,  7th,  &c.,  including  all  the  odd  numbered  breadths, 
except  the  first  and  last,  by  2 ;  to  the  sum  of  these  products  add 
the  first  and  last  breadths  ;  this  quantity  multiplied  by  one-third 
of  the  common  interval  between  the  breadths  gives  a  mean  hori- 
zontal area  of  the  space  between  decks  ;  which,  being  multiplied 
by  the  height  between  the  two  decks,  gives  the  cubical  content ; 
and  this,  divided  by  one  hundred,  gives  the  register  tonnage  of 
the  space  required. 


36 


ADMEASUREMENT    OF    TONNAGE. 


Example  of  Computation. 

Suppose  the  inside  length  at  the  middle  of  the  height  to  be  96 
feet ;  this,  being  divided  into  eight  equal  parts,  gives  twelve  feet 
for  the  common  interval  between  the  breadths,  so  that  one-third 
of  the  commoji  interval  is  four  feet. 

Suppose,  also,  the  height  of  the  space  to  be  seven  feet,  and 
the  breadths  measured  as  above  directed,  to  be  as  set  forth  in  the 
formula  below,  the  process  is  then  as  follows  : — 


GENERAL  FORMULA. 

Length  96  ft,  -5-  8  =  12  ft.  the 
com.  int.  betn.  breadths. 

No. 

Multi- 
pliers. 

Breadths. 

Products. 

1 

1 

1 

1 

2 

4 

22 

88 

3 

2 

24 

48 

4 

4 

25 

100 

5 

2 

26 

52 

6 

4 

25 

100 

7 

2 

24 

48 

8 

4 

23 

92 

9 

1 

22 

22 

551 
4  is  £  of  12,  com.  int.  between  breadths. 

2204  mean  horizontal  area  of  space. 
7  height  of  space. 


Cubic  content  15428  -5-  100  =  154.28  tons,  register  tonnage 
of  space  between  spar  and  tonnage  deck. 


DIRECTIONS    FOR    MEASURING    VESSELS.  37 

GENERAL  DIRECTIONS  FOR  TAKING  THE    MEAS- 
UREMENTS   OF    VESSELS. 

The  correctly  taking  of  the  required  measurements  being  of 
considerable  importance,  the  following  general  directions  to  that 
end  may  be  useful  for  the  guidance  of  those  who  have  not  a  pro- 
fessional acquaintance  with  the  subject : — 

Length. — The  length  at  the  tonnage-deck  is  to  be  taken  by 
tightly  stretching  a  line  on  the  upper  surface  of  the  deck,  at  such 
a  parallel  distance  from  the  middle  line  of  the  ship  as  to  clear  the 
several  hatchways  and  other  obstacles  that  may  present  them- 
selves ;  the  line  is  then  to  be  measured,  marking  the  ends  of  the 
line  on  the  deck  ;  these  points  are  then  to  be  squared  in  to  the 
middle  line  of  the  ship,  and  the  distances  taken  from  them  so 
squared  in,  to  the  inside  of  the  plank  at  the  bow  and  stern, 
deducting  from  this  length  what  is  due  to  the  rake  of  the  bow  in 
the  thickness  of  the  deck,  and  what  is  due  to  the  rake  of  the 
stern-timber  in  the  thickness  of  the  deck,  and  also  what  is  due 
to  the  rake  of  the  stern-timber  in  one-third  of  the  round  of  the 
beam  ;*  the  sum  of  these  two  distances  added  to  the  length  of  the 
line  measured,  as  aforesaid,  gives  the  whole  length  required. 

Points  of  Division  of  the  Length,  or  Stations  of  the  Transverse 
Areas. — The  length,  taken  as  above  described,  being  divided  into 
the  required  number  of  equal  parts,  the  points  of  division,  which 
are  the  stations  of  the  areas,  are  to  be  marked  correctly  on  the 
tonnage-deck  :  a  line  is  then  to  be  extended  down  the  main  hatch- 
way, at  the  middle  line  of  the  ship,  in  a  direction  perpendicular 
to  the  keel,  by  means  of  a  square  placed  on  the  upper  side  of  the 
keelson  ;  the  distance  of  the  midship  area  from  this  line  at  the 
tonnage-deck  is  then  to  be  set  off  from  this  line  on  the  keelson, 
which  gives  the  station  of  the  midship  area  on  the  keelson  ;  and 
the  stations  of  the  others  are  obtained  on  the  keelson  by  setting 
off  afore  and  abaft  the  midship  one,  the  common  interval  between 
them,  as  already  marked  off  on  the  tonnage-deck. 

*  This  is  to  give  the  length  at  the  medium  height  of  deck. 
Bl  4 


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Cubic  Content  and 
Register  Tonnage. 

IJ 

0 

(N    CO 

s| 

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3 

in 

3 

p 

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GENERAL  FORMULA. 

Length,  100  feet  -=-  8  =  12.5  feet,  common  interval  between  areas. 

j 

5 

o 

£ 

ic 

G 

I 
O, 

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1 
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0 

ESSENTIAL    QUALITIES.  43 

ESSENTIAL    QUALITIES    OF    THE    LAW. 

Having  thus,  at  length,  given  such  illustrations  and  examples 
as  appeared  to  be  necessary  to  prove  the  correctness  of  the  pro- 
cess, and  show  the  mode  of  its  application  to  those  parts  of  vessels 
which  require  to  be  measured;  there  now  only  remains  to  describe 
some  essential  qualifications.  These  qualifications  are  summarily 
enumerated  as  follows  : — 

The  evasion  of  Lawful  Tonnage  is  prevented. 
This  is  accomplished  by  the  number  and  position  of  the  pre- 
cribed  measurements  ;  these  may  be  considered  rather  numerous 
for  a  practical  operation  ;  but,  on  this  point,  it  is  to  be  borne  in 
mind,  that  it  has  been  found  absolutely  necessary  to  employ  a 
multiplicity  of  measurements  to  insure  the  effectual  prevention, 
by  ingenious  constructors,  of  so  altering  the  forms  of  vessels  be- 
tween the  measurements,  as  to  evade  thereby  a  just  expression 
of  the  tonnage. 

Inducement  to  construction  of  ill-formed  Vessels  removed. 

This  is  effected  by  the  prescribed  measurements  reaching  every 
peculiarity  of  form  which  can  be  devised  of  the  least  importance 
as  affecting  the  capacity  ;  whereas,  under  the  operations  of  the 
rules  hitherto  established,  it  is  only  necessary,  in  consequence  of 
the  position  and  paucity  of  their  measurements,  to  increase  unduly 
those  dimensions  which  are  unaffected  by  the  law,  and  an  excess 
of  capacity  is  attained  without  detriment  to  the  register  tonnage ; 
while,  at  the  same  time,  the  sailing  and  seaworthy  qualities  of 
the  vessel  may  be  thereby  seriously  compromised. 

As,  however,  by  the  new  mode,  no  such  advantage,  as  capac- 
ity independent  of  register  tonnage,  is  attainable,  there  will  be 
no  longer  any  inducement  to  give  other  forms  to  vessels  than 
those  tending  best  to  develop  the  maximum  advantage  to  be 
derived  by  a  judicions  blending  of  their  sailing  and  carrying  re- 
quirements. 

Tonnage  in  proportion  to  capacity  obtained. 

A  just  and  true  relative  expression  of  Register  Tonnage  in 
proportion  to  capacity  is  effected,  whatever  may  be  the  nature  of 
the  materials  used  in  the  building,  or  whatever  the  form  of  the 
vessel  may  be  : — This  important  desideratum  is  assured  by  the 
great  degree  of  accuracy  which  the  system  affords  in  ascertaining 
the  true  capacities  of  vessels. 

Wrong  measurement  can  be  detected. 

Wrong  measurement,  whether  by  design  or  accident,  can,  at 
any  time,  be  detected  : — This  is  derived  from  the  innate  proper- 


44  ESSENTIAL   QUALITIES. 

ties  of  the  plan,  and  is  accomplished  by  means  of  the  formula 
used  in  the  operation  of  measurement.  By  means  of  this  formula 
detective  curves  can,  at  any  time,  be  easily  and  quickly  con- 
structed ;  showing  where  any  error,  if  any  of  material  importance, 
has  been  introduced. 

Cubic  Feet  in  Hold  ascertained. 

We  know,  for  instance,  that  in  the  register  tonnage  of  a  vessel 
computed  by  the  new  mode,  every  ton  must  consist  exactly  of 
100  cubic  feet ;  therefore,  to  ascertain  the  number  of  cubic  feet  in 
a  vessel's  hold  under  the  tonnage-deck,  it  is  only  necessary  to  add 
two  ciphers  to  the  right  of  the  figures  expressing  the  register 
tons  under  that  deck,  and  the  number  of  cubic  feet  in  the  hold  is 
at  once  shown  : 

For  example,  suppose  the  register  tonnage  under  the  tonnage- 
deck  of  a  vessel  to  be  619  tons,  then  61900  cubic  feet  is  the  cubi- 
cal content  of  her  hold. 

Measurement  of  Cargo  ascertained. 

Again,  To  find  the  Number  of  Tons  of  Export  Measurement 
Goods  of  40  cubic  feet  to  the  ton,  which  a  vessel  is  enabled  to  take  or 
stow,  it  is  only  to  divide  the  above  number  of  cubic  feet  by  40, 
having  first  made  the  proper  deduction  due  to  the.  spaces  which 
may  be  occupied  by  the  crew,  store-rooms,  provisions  and  water, 
pump-well,  beams,  &c.,  &c. ;  which,  on  the  whole,  may,  practi- 
cally speaking,  be  estimated  to  amount  to  about  twenty  per  cent.* 
or  one-fifth  of  the  whole  cubic  content  under  the  tonnage-deck. 

For  example,  the  register  tonnage  under  the  tonnage-deck 
being  as  before  619  tons,  the  cubic  content  of  the  hold  is  61900 
cubic  feet,  and  61900  minus  (61900  divided  by  5)  equal  49520  net 
cubic  content,  and  49520  divided  by  40  equal  1238  tons,  the 
quantity  of  export  measurement  goods  that  can  be  stowed.  Or, 
in  the  case  of  import  goods  at  50  cubic  feet  to  the  ton,  we  have 
49520  divided  by  50  equal  99.0  tons. 

Weight  of  Cargo  ascertained. 

And  again,  If  the  Deadweight  which  a  vessel  can  carry  be  re- 
quired, a  useful  approximation  is  obtained  by  dividing  the  number 
of  cubic  feet  in  the  hold,  as  above,  by  63  ;  from  which  result  must 
be  taken  the  weights  of  the  water,  provisions,  crew,  and  their 

*  Of  which  20  per  cent.  2|  maybe  considered  as  due  to  the  space  occupied  by 
the  crew  ;  65  as  due  to  twelve  months'  provisions  and  water  in  the  usual  pro- 
portion ;  3  as  due  to  beams,  knees,  shelf-pieces,  pillars,  keelson,  &c..  &c. ;  nnd 
8  per  cent,  to  p^tiy  officers'  accommodation,  storerooms,  and  dunnage.  Mr. 
Henry  Cleaver  Chapman,  an  experienced  ship-owner  of  Liverpool,  considers 
that  25  per  cent,  may  be  deducted  from  the  entire  cubic  content  of  the  hold,  as  a 
fair  allowance  for  these  various  items  and  impediments  to  stowage. 


THICKNESS  OF  THE  SHELLS  OR  SIDES  OF  VESSELS.  45 


effects  ;  which,  in  the  case  of  being  provisioned  for  twelve  months, 
may,  practically  speaking,  be  estimated  to  amount  to  about  7-per 
cent.,  or  one-fourteenth  of  the  above  result : 

For  example,  the  register  tonnage  under  the  tonnage-deck 
being  as  before  619  tons,  the  cubic  content  of  the  hold  is  61900 
feet,  and  61900  divided  by  63  equal  982  tons,  the  gross  weight  of 
water,  provisions,  dunnage,  and  cargo,  and  982  minus  (982  di- 
vided by  14)  equal  912  tons,  the  net  weight  of  cargo  and  dunnage. 


PROPORTIONS    OF    SHELLS    OF   SHIPS  TO    THEIR 
INTERNAL    CAPACITIES. 

Tables  and  Remarks  connected  ivith  the  thickness  of  the  Sides  or 
Shells  of  vessels  built  of  different  materials,  as  Oak,  Fir  and  Iron. 

TABLE  No.  1.— Showing  the  Cubic  Contents  of  the  Hulls,  to  the 
height  of  the  upper  Deck,  of  Oak-built  vessels,  measured  first  to 
the  outside  of  the  Sides  or  Shell,  and  then  to  the  inside  (the  differ- 
ence showing  the  Cubic  Contents  of  the  Shells) ;  showing,  also,  the 
Proportions  which  the  Shells  bear  to  their  respective  Internal 
Capacities  ;  these  proportions  being  necessary  data  in  the  following 
remarks  and  subsequent  investigations. 


DESCRIPTION 
OF   VESSEL. 

Register 
Tonnage, 
New 
Mode. 

Cubic  contents  of  the 
lull  to  the  height  of  the 
upper  deck,  measured 
to  the  outside,  also  to 
the  inside,  of  the  sides 
or  shell. 

Cubic 
contents 
of  the 
sides  or 
shell. 

Proportion 
of  the  shell 
to  ihe  in- 
ternal ca- 
pacity. 

East  Indiaman 
with  three  decks. 
Old  usual  form. 

Tons. 
1469.9 

Cubic  feet. 
Out.  173482.61  to  spar 
In.     146900.85       deck 

Diff.    26491.76 

Cubic  ft. 
26491.7 

Per  cent. 
18 

East  Indiaman 
with  three  decks. 
Unusually  sharp. 

1419.5 

Out.  171586.46  to  spar 
hi.     141346.80       deck 

30239.66 

30239.66 

21.4 

East  Indiaman 
with  two  decks. 
Rather  sharp  and 
shallow. 

1057.2 

Out.  115986 
In.       95155.48 

20830.52 

20830.52 

21.9 

Coasting  Brig. 
Usual  form. 
RaUier  shallow. 

98.6 

12462 
9703.96 

2758.04 

28.4 

2758.04 

Fruit  Schooner. 
Very  sharp  and 
shallow. 

109.8 

13737 
10554.4 

3182.6 

3182.6 

30.1 

46 


MEDIUM    THICKNESS    OF    THE    SIDES    OF    VESSELS. 


MEDIUM  THICKNESS  OF  THE  SIDES  OF  VESSELS. 

The  following  Table,  showing,  generally,  the  Proportion  of  the  Oak 
Shells  to  the  Internal  Capacities  in  vessels  of  the  usual  form  ;  also 
the  medium  Thicknesses  of  the  Shells  of  Oak,  Fir,  and  Iron-built 
vessels,  is  constructed,  in  its  three  first  columns,  upon  the  basis  of 
the  preceding  Table,  and  in  its  two  last  columns  upon  Mr.  Creuze's 
official  Report,  from  the  Office  of  Lloyd's  Register  of  British  and 
Foreign  Shipping,  to  the  Board  of  Trade  : — 

TABLE  No.  2. 


1 

Tonnage 
New  Mode. 

2 

Proportion  of 
the  oak  shell  to 
the  internal 
capacity. 

3 

Medium 
thickness  ot' 
the  sides  of 
oak  vessels. 

4 
Medium 
thickness  of 
the  sides  of 
fir  vessels. 

5 

Medium 
thickness  of 
the  sides  of 
iron   vessels. 

Tons. 
1400 

Per  cent. 

18 

Inches. 
22.26 

Inches. 

Inches. 

7 

1000 

20.5 

20.88 

28.42 

6.96 

700 

22.5 

18.5 



* 

600 

23.25 

17.28 

22.2 

* 

500 

24 

16.44 

21.12 

5.48 

400 

25 

15.5 

19.68 



300 

26 

14.7 





200 

27 

12.9 

17.68 

4 

100 

28 

11.16 





*j  And,  generally  speaking,  the  sides  of  iron  vessels  may  be  considered  to  be 
about  one-third  of  the  thickness  of  the  sides  of  oak  vessels  of  equai  tonnage. 

REMARKS  ON  THE  RESULTS  IN  THE  PRECEDING  TABLES, 
Nos.   I  AND  2. 

ART.  1.  In  comparing-  the  results  in  the  foregoing  Table,  No. 
1,  it  is  seen,  in  the  case  of  the  two  large  Indiamen,  that  their 
tonnage,  or  true  proportionate  capacities,  are  the  same  within 
about  fifty  tons,  while,  at  the  same  time,  one  of  the  vessels  is  of 
the  usual  full  form,  and  the  other  unusually  sharp.  The  capac- 
ities being  so  nearly  the  same,  it  is  manifest  that  the  sharp  vessel 
must  be  greater  in  her  principal  dimensions  to  make  up  for  her 
fineness  in  form ;  and  we  accordingly  find,  in  comparing  the  di- 
mensions, that  she  has  an  additional  length  of  about  twelve  feet. 

Reverting  to  the  Table,  it  is  observed,  that  in  the  full  formed 
vessel  the  shell  is  eighteen  per  cent  of  the  capacity,  while  in  the 


REMARKS    ON    RESULTS    IN    PRECEDING    TABLES.          47 

other  the  proportion  of  shell  to  capacity  is  raised  to  twenty-one 
and  a  half  per  cent ;  showing,  that  in  long  sharp  vessels  of  this 
class,  the  quantity  of  timber  in  the  frame  is  greater  than  in 
fuller  and  shorter  vessels  of  the  same  capacity  or  tonnage,  by 
about  three  and  a  half  per  cent  of  the  tonnage. 

2.  Again,  comparing  the  Coasting  Brig  and  Fruit  Schooner, 
of  98  and  109  tons  respectively,  the  former  of  the  usual  form,  and 
the  latter  of  the  sharpest  model,  (the  sharpness  being  balanced, 
as  in  the  above  case  of  the  large  vessels,  by  an  addition  of  ten 
feet  in  length,)  we  see  a  difference  of  more  than  one  and  a-half 
per  cent  in  the  ratio  of  shell  to  capacity ;  proving,  that  in  vessels 
of  the  smaller  class,  as  well  as  in  those  of  the  larger,  a  greater 
quantity  of  timber  is  expended  in  the  frame  of  long  sharp  vessels 
than  in  shorter  and  full-formed  vessels  of  equal  capacity. 

3.  Looking,  generally,  at  the  Table,  No.  1,  there  appears,  in 
regard  to  vessels  of  the  usual  form,  to  be  a  certain  gradation,  in 
the  proportion  of  shell  to  capacity,  through  the  various  classes  ; 
the  difference  of  that  ratio  between  the  largest  and  smallest  ves- 
sel in  the  Table  being  about  ten  per  cent. 

Resulting  from  these  considerations,  the  following  facts  appear 
to  be  established  : — 

More  Timber  in  the  frames  of  long  sharp  Vessels  than  in  short 
full  ones  of  equal  tonnage. 

(a).  That  long  sharply  formed  vessels  of  the  larger  class  re- 
quire more  timber  in  the  construction  of  their  frames,  to  the 
amount  of  one,  two,  or  three-and-a-half  per  cent  (according  to 
their  sharpness)  of  their  internal  capacity,  than  short  full-formed 
vessels  of  the  same  tonnage  or  capacity  (tonnage  and  capacity, 
by  the  new  mode,  being  always  in  the  same  proportion)  ;  and  in 
the  smaller  class  of  vessels,  from  one  to  one-and-a-half  per  cent. 

In  the  usual  form  of  Vessels,  the  larger  the  Vessel  the  less  Timber 
in  the  frame  in  proportion  to  tonnage. 

(b).  And  that,  in  vessels  of  the  usual  form,  the  larger  the 
vessel  the  less  timber,  in  proportion  to  capacity  or  tonnage,  is 
required  for  the  frame,  by  about  three-quarters  per  cent  (on  an 
average)  of  the  capacity,  for  every  one  hundred  tons  increase. 

Timber  in  the  frame  of  a  Vessel  approximately  estimated. 

4.  With  regard  to  Table,  No.  2,  a  due  consideration  of  the 
results  in  the  2nd  column  (which  are  a  digest  of  the  results,  in 
reference  to  the  usual  form  of  vessels,  in  Table,  No.  1)  may, 


48          REMARKS    ON    RESULTS    IN    PRECEDING    TABLES. 

occasionally,  be  found  useful  to  the  interests  of  the  merchant 
shipbuilder.  And  holding  them  as  general  data,  their  utility 
(in  conjunction  with  correct  admeasurement)  will  be  perceived 
from  the  consideration,  that  if  the  tonnage  of  a  vessel,  agreeably 
to  the  new  mode,  or  any  equally  correct  mode,  be  fixed  upon, 
the  quantity  of  converted  timber  required  for  the  construction  of 
her  frame,  can  be  pretty  well  estimated  by  their  instrumentality. 
Supposing,  for  instance,  the  tonnage,  as  above  stated,  to  be 
given,  it  is  only  necessary  to  add  two  ciphers  to  the  right  of  the 
integral  figures,  and  we  have  the  internal  capacity  in  cubic  feet ; 
the  respective  per  centage  of  which  is  then  taken,  as  directed  in 
column  2,  which  will  give  the  approximate  cubical  content  of  the 
shell,  or  quantity  of  Converted  timber  required  for  the  construc- 
tion of  the  frame ;  observing,  at  the  same  time,  that  if  the  model 
of  the  vessel  be  sharper  (a)  than  the  usual  form,  1,  2,  or  even, 
in  the  case  of  large  vessels,  3  per  cent  more  of  the  capacity,  ac- 
cording to  the  degree  of  sharpness,  must  be  added  to  the  above 
result,  observing,  however,  that  the  small  extra  quantity  above 
the  upper  deck  will,  in  all  cases,  remain  to  be  estimated  and 
added  hereto. 

The  following  are  Examples  illustrative  of  the  above  proposition. 

Example  1. — The  tonnage  of  a  vessel  of  the  usual  form,  agree- 
ably to  the  new  mode,  is  1469.9,  say,  1470  tons,  what  is  the  ap- 
proximate quantity  of  timber  contained  in  her  shell  or  frame  ? 
1470  ions  X  1°0  =  147000  cubic  feet,  internal  capacity. 

Then  (column  2)  18  per  cent  on  147000  cubic  feet  =  26460 
cubic  feet,  the  approximate  quantity  of  timber  required  ;  which 
is  n  result  within  32  cubic  feet  of  the  shell  of  this  vessel  given 
in  Table  1. 

Example  2. — Suppose  the  tonnage  of  a  vessel  of  the  usual 
form,  agreeably  to  the  new  mode,  to  be  1419  tons,  what  is  the 
approximate  quantity  of  timber  in  her  frame? 

1419  tons  X  10°  =  141900  cubic  feet,  internal  capacity. 

Then  (column  2)  18  per  cent  on  141900  cubic  feet  =  25542 
cubic  feet,  the  approximate  quantity  of  timber  required,  in  the 
frame  of  a  vessel  of  the  usual  form,  of  the  above  tonnage. 

But  supposing,  on  the  other  hand,  the  vessel  to  be  of  an  un- 
usually sharp  construction,  and  of  the  same  tonnage  as  above, 
then  (a)  an  addition  of  3^  per  cent  of  the  capacity  must  be  made 
to  the  above  quantity  ;  and  as  3^  per  cent  on  141900  cubic  feet 
is  4966  cubic  feet,  we  have 

25542  cubic  feet  +  4966  cubic  feet  =  30508  cubic  feet. 


ADVANTAGE    GIVEN    BY   EXTERNAL    MEASUREMENT.      49 

the  approximate  quantity  of  timber  required,  in  the  case  of  a  very 
sharp  vessel  of  this  class.  This  result  differs  only  about  268 
cubic  feet  from  the  cubical  content  of  the  shell  of  this  vessel, 
given  in  Table,  No.  1. 

Example  3. — The  tonnage  of  a  vessel  of  the  usual  form,  by 
new  mode,  being  109  tons,  what  is  the  approximate  quantity  of 
timber,  in  her  shell  or  frame  ? 

109  tons  X  100  =  10900  cubic  feet,  internal  capacity. 

Then  (column  2)  28  per  6ent  on  10900  cubic  feet  =  3052 
cubic  feet  the  approximate  quantity  of  timber  required  in  the 
frame  of  a  vessel,  of  the  usual  form,  of  the  above  tonnage. 

But  supposing,  on  the  other  hand,  the  vessel  to  be  of  a  very 
sharp  model,  a  sharp  Fruit  Schooner,  for  instance,  and  of  the 
same  tonnage  as  above,  then  (a)  an  addition  of  1^  per  cent  of  the 
capacity  must  be  made  to  the  above  quantity  ;  and  as  1-|  per  cent 
on  10900  cubic  feet  is  163.5  cubic  feet,  we  have 

3052  cubic  feet  -f- 163.5  cubic  feet  =  3215.5  cubic  feet. 

the  approximate  quantity  of  timber  required  in  the  frame  of  a 
sharp  vessel  of  this  class  ;  which  is  a  result  within  33  cubic  feet 
of  the  shell  of  this  vessel,  given  in  Table,  No.  1. 

The  utility  of  such  practical  estimates  as  the  one  here  investi- 
gated, and  as  are  found,  also,  described  at  pages  43  and  44, 
render  further  apparent  the  advantages  of  a  correct  system 
of  admeasurement.  No  approximate  system,  framed  mainly  for 
the  sake  of  brevity,  and  ease  of  computation,  could  afford  suffi- 
cient correctness,  or  inspire  the  confidence  necessary  to  render 
such  collateral  processes  of  any  real  practical  advantage. 


ADVANTAGE    GIVEN,    BY    EXTERNAL    MEASURE- 
MENT,   TO    THIN-SIDED   VESSELS. 

Investigation,  showing,  in  the  case  of  Vessels  of  the  same  external 
form  and  dimensions,  built  severally  of  Oak,  Fir,  and  Iron,  what 
is  the  effect  of  the  difference  in  the  thickness  of  their  sides  or  shell, 
on  their  internal  capacities  for  Stowage  ;  proving  the  advantage 
given  by  external  measurement  to  thin-sided  Vessels. 

The  three  classes  of  vessels,  of  1000,  500,  and  200  tons,  being 
considered  sufficient  for  the  purposes  of  the  investigation,  the  fol- 

Bl  5 


50      ADVANTAGE    GIVEN    BY  EXTERNAL    MEASUREMENT. 


lowing  Table,  having  reference  thereto,  and  which  is  derived 
from  the  columns  of  the  preceding  Table,  No.  2,  has,  therefore, 
been  extended  only  to  those  classes. 

TABLE  No.  3. 


Class  of 
Vessels. 

1 

Amount  per  cent 
of  the  Internal 
Capacity  that  is 
due  to  one  inch 
of  thickness  of 
the  Shell. 

2 

No.  of  Inches 
that  the  Shell  of 
ihe  Oak  Vessel 
is  thinner  than^ 
that  of  the  Fir 
Vessel. 

3 

No.  of  Inches 
that  the  Shell  of 
the  Iron  Vessel 
is  thinner  than 
that  of  the  Oak 
Vessel. 

4 
No.  of  Inches 
that  the  Shell  of 
ihe  Iron  Vessel 
is  thinner  than 
that  of  the  Fir 
Vessel. 

Tons. 
1000 

Per  Cent.- 
1  nearly. 

Inches. 
7.54 

Inches. 
14  nearly. 

Inches. 
21.46 

500 

1.46 

4.68 

10.96 

15.64 

200 

.2.09 

4.73 

8.9 

13.68 

Suppose  three  vessels,  in  each  of  the  above  classes,  to  be  built, 
severally,  of  oak,  fir,  and  iron,  of  the  same  external  form  and 
dimensions  in  every  respect. 

ART.  1  —  In  the  case  of  Vessels  of  1000  Tons. 

Istly.  Comparing  the  oak  and  fir  vessels  together:  the  oak 
vessel,  beinp:  thinner  in  her  shell  than  the  fir  vessel  by  7.54  ins. 
(column  2),  is  larger  in  her  internal  capacity  to  that  extent,  and 
as  one  per  cent  is  due  to  every  inch  of  the  thickness  of  the  shell 
(column  1),  the  oak  vessel  exceeds  the  fir  vessel  in  internal  ca- 
pacity by  1  per  cent  X  7.54  =  7.54  per  cent.  Consequently, 
while  under  any  system  of  external  measurement,  the  register 
tonnage  of  these  two  vessels  would  be  precisely  the  same,  the 
oak  vessel  would  have  the  advantage  in  capacity  for  stowage  of 
cargo,  to  the  amount  of  7.54  per  cent. 

And  2ndly,  Comparing  the  oak  and  iron  vessels  :  the  iron  ves- 
sel being  thinner  in  her  shell  than  the  oak  vessel  by  fourteen 
inches  (column  3),  she  is  larger  in  her  internal  capacity  to  the 
extent  of  1  per  cent  X  14  =  14  per  cent ;  and  therefore,  under 
external  measurement,  the  iron  vessel  will  have  this  advantage 
over  the  oak  vessel. 

And  Srdly.  With  regard  to  the  fir  and  iron  vessels  :  the  iron 
vessel  being  thinner  in  her  shell  than  the  fir  vessel  by  21.46 
inches,  she  is  larger  in  her  internal  capacity  to  the  extent  of  1 
per  cent  X  21.46  =  21.46  per  cent;  and  therefore,  under  ex- 
ternal measurement,  the  iron  vessel  will  have  this  advantage  over 
the  fir  vessel. 


ADVANTAGE    GIVEN    BY   EXTERNAL    MEASUREMENT.       51 

2.— In  the  case  of  Vessels  0/500  Tons. 

Istly.  Comparing  the  oak  and  fir  vessels  :  as  the  former  is  thin- 
ner in  her  shell  by  4.68  inches  (column  2),  and  as  1.46  per  cent 
of  the  internal  capacity  is,  in  this  class,  due  to  every  inch  of 
thickness  (column  1),  the  oak  vessel,  therefore,  exceeds  the  fir 
vessel  in  internal  capacity  by  1.46  per  cent  X  4.68  =  6.8  per 
cent;  and  therefore  has  the  advantage,  to  this  extent,  under  ex- 
ternal measurement. 

And  2ndly.  Comparing  the  oak  and  iron  vessels  :  as  the  shell 
of  the  latter  is  thinner  than  that  of  the  former  by  10.96  inches, 
its  internal  capacity  is  greater  by  1.46  per  cent  X  10.96  =  16 
per  cent ;  and  therefore  the  iron  vessel  has  the  advantage  of  the 
oak  vessel  to  this  extent. 

And  3rdly.  Comparing  the  fir  and  iron  vessels  :  as  the  shell  of 
the  latter  is  thinner  than  that  of  the  former  by  15.64  inches,  its 
internal  capacity  is  greater  by  1.46  per  cent  X  15.64  =  22.8  per 
cent ;  and  therefore  the  iron  vessel  has  the  advantage  of  the  fir 
vessel  to  this  extent. 

3.— In  the  case  of  Vessels  0/200  "Ions. 

Istly.  Comparing  the  fir  and  oak  vessels  :  the  shell  of  the  lat- 
ter is  4.78  inches  thinner  than  that  of  the  former  ;  and  as  in  this 
class  of  vessels  2.09  per  cent  of  the  internal  capacity  is  due  to 
every  inch  of  the  thickness  of  the  shell  (column  1),  therefore  the 
internal  capacity  of  the  oak  vessel  is  greater  by  2.09  per  cent  X 
4.78  =  10  per  cent ;  and  therefore  the  oak  vessel  has  the  advan- 
tage of  the  fir  vessel  to  this  extent. 

2ndly.  Comparing  the  oak  and  iron  vessels :  the  shell  of  the 
latter  being  thinner  than  that  of  the  former  by  8.9  inches,  its  in- 
ternal capacity  is  greater  by  2.09  per  cent  X  8.9  =  18.6  per 
cent ;  and  therefore  the  iron  vessel  has  the  advantage  of  the  oak 
vessel  to  this  extent. 

Srdly.  Comparing  the  fir  and  iron  vessels  :  the  shell  of  the  lat- 
ter being  thinner  than  that  of  the  former  by  13.68  inches,  its  in- 
ternal capacity  is  greater  by  2.09  per  cent  X  13.68  =  28.6  per 
cent ;  and  therefore  the  iron  vessel,  under  external  measurement, 
has  the  advantage  of  the  fir  vessel  to  this  amount. 

Synopsis  of  the  advantages  which  thin-sided  vessels  have  over  thick- 
sided  vessels. 

4.  Synopsis  of  the  preceding  investigation,  showing,  in  a  tab- 
ular form,  the  advantage  in  reference  to  capacity  for  stowage 
(under  any  system  of  external  measurement)  which  oak-built 
vessels  have  over  those  built  of  fir,  also  the  advantage  which 
iron-built  vessels  have  over  both. 


52 


WEIGHTS  OF  THE  HULLS  OF  VESSELS. 


TABLE  No.  4. 


Class  of 
Vessels. 

Advantage  of  Oak 
over  Fir  Vessels. 

Advantage  of  Iron 
over  Oak  Vessels. 

Advantage  of  Iron 
over  Fir  Vessels. 

Tons. 
1000 

Per  Cent. 
7.54 

Per  Cent. 
14 

Per  Cent. 
21.46 

500 

6.8 

16 

22.8 

200 

10 

18.6 

28.6 

WEIGHTS    OF  THE  HULLS  OF  IRON  AND  WOOD- 
BUILT    VESSELS. 

The  Weights  of  the  Hulls  of  Iron  and  Wood  (Oak)  built  Vessels  com- 
pared, showing  the  effects  of  their  difference  of  buoyancy  in  the  in- 
creased weight  of  cargo  which  Iron  Vessels  are  enabled  to  carry. 

From  the  difficulty,  it  may  almost  be  said  from  the  impossibil- 
ity, of  procuring' the  requisite  data  for  directly  comparing  the 
buoyancy  of  iron  and  wood  vessels  (such  data  consisting  of  the 
exact  weights  of  sister  ships  of  different  sizes,  built  of  each  kind 
of  material,  alike  respectively  in  every  other  respect),  it  has,  for 
this  reason,  been  found  necessary  to  have  recourse  to  the  more 
indirect  means  of  inductive  calculations. 

The  data  at  hand,  being  from  a  responsible  official  source,  and 
therefore  to  be  depended  upon  for  correctness,  consist  of  the 
weights  of  the  wood  and  iron  hulls  of  various  war  steamers,  from 
the  "largest  to  the  smallest  size,  and  of  their  tonnage  under  the 
old  measurement,  or  builder's  tonnage,  as  it  is  frequently  termed. 

The  method  of  obtaining  from  these  data  the  comparaiive  buoy- 
ancy of  the  two  kinds  of  vessels  is  as  follows  : 

The  vessels  from  which  these  calculations  have  been  obtained, 
being  wholly  vessels  of  war,  may  be  considered  of  similar  form, 
and  therefore  the  internal  and  external  capacities  are,  practically 
speaking,  in  proportion  to  their  length,  breadth  and  depth  jointly  ; 
consequently  their  differences,  namely,  the  hulls  or  weights  of 
the  hulls,  (considering  the  hulls  to  be  homogeneous,)  are  in  the 
same  proportion.  But  the  old  tonnage  is  in  proportion  to  the 
length,  breadth  and  depth  jointly  (considering  the  depth  to  be  in 
proportion  to  the  half  breadth),  consequently  the  weights  of  the 
hulls  are  in  proportion  to  the  old  tonnage. 

Therefore  it  is  only  necessary  to  find,  from  the  table  annexed, 
the  mean  tonnage  of  each  of  the  two  kinds  of  vessels,  also  the 
mean  weights  of  their  hulls  respectively  ;  and  their  comparative 


WEIGHTS    OF    IRON    AND   WOOD-BUILT    VESSELS. 


53 


buoyancy  is  thence  readily  ascertained  by  means  of  simple  pro- 
portions. 


The  Light  Displacements  or  Weights  of  the  Hulls  of  several  War 
Steam  Vessels,  shown  under  their  respective  heads  of  Iron-built 
and  Wood-built  Vessels  ;  also  the  old  or  Builders'  Tonnage  of  the 
same,  in  reference  to  ascertaining  the  comparative  buoyancy  of 
Iron-built  and  Wood-built  Vessels. 

TABLE  No.  5. 


IRON-BUILT  VESSELS. 

WOOD-BUILT  VESSELS. 

Ships' 
Names. 

Weight 
of  Hulls. 

Old  Reg. 
Tonnage. 

Ships' 
Names. 

Weight 
of  Hulls. 

Old  Reg. 
Tonnage. 

Simoon   . 
Vulcan    . 

Tons. 
1350 
1000 

Reg.  T's. 
1980 
1764 

Arrogant 
Terrible  .     . 

Tons. 
1190 
1420 

Reg.  Tons. 
1872 
1847 

Greenock     . 

955 

1413 

Retribution  . 

1275 

1641 

Birkenhead 

917 

1405 

Dauntless     . 

1010 

1497 

Megara   . 

753 

1397 

Amphion 

977 

1474 

Trident   . 

385 

850 

Avenger  .     . 

1160 

1444 

Triton     . 

394 

654 

Odin  .     .     . 

1070 

1310 

Antelope 

390 

650 

Magicienne  . 

973 

1255 

Oberon    . 

383 

649 

Conflict   •     . 

740 

1058 

Grappler 

294 

557 

Buzzard 

749 

997 

Sharpshooter 

204 

503      . 

Archer    . 

602 

970 

Jackall     .     / 

180 

340 

Phoenix  •     . 

660 

809 



Acheron  . 

337 

722 

12)7205 

12)12162 

Volcano  .     . 

407 

QQft 

720 

600.42 

1013.5 
Mean 

Reynard  .     • 
Rifleman 

OOU 

256 

486 

weight. 

Register 

16)13156 

16)18618 

onnage. 

822.25 

1163.62 

Mean 

Mean  Reg. 

Weight. 

Tonnage. 

From  the  above  results  we  derive  the  following  proportions  : — 


Reg.  Ton.  :  Weight  of  Iron  Hull  =  1013  5    :  600.42  =  1 
Reg.  Ton.  :  Weight  of  Wood  Hull  =  1163.62  :  822.25  =  1 


.5924 
.7066 


Hence  it  is  manifest  that 

Weight  of  Iron  Hull  :  Weight  of  Wood  Hull  =  .5924  :  .7066 


Or  algebraically,  thus : — 


Weight  of  Iron  Hull  --'Reg.  Ton.  =    .5924 
Reg.  Ton.  :  Weight  of  Wo.  Hull  =  1 


.7066 


Striking  out  the  antecedent  and  consequent  aequales 
Weight  of  Iron  Hull  :  Weight  of  Wood  Hull 


.5924  :  .7066 


Bl 


5* 


54         WEIGHTS    OF    IRON    AND   WOOD-BUILT    VESSELS. 

In  Steam  Vessels  Iron  Hull  more  buoyant  than  Wood  Hull. 

That  is,  while  the  weight  of  the  iron  hull  is  expressed  by  the 
quantity  .5924,  the  weight  of  the  wood  hull  is  relatively  ex- 
pressed by  the  quantity  .7066  ;  and  therefore  the  difference  be- 
tween the  two,  namely,  .1142,  is  the  relative  quantity  by  which 
the  iron  hull  is  lighter  or  more  buoyant  than  the  hull  built  of 
wood.  But  .1142  is  16.16  per  cent  on  .7066,  the  weight  of  the 
wood  hull ;  therefore — 

In  the  case  of  steam  vessels,  the  vessel  built  of  iron  is  more 
buoyant  than  the  vessel  built  of  wood,  by  about  16  per  cent  of 
the  weight  of  the  wood  hull. 

The  above  result,  being  founded  on  data  derived  solely  from 
steam  vessels,  the  wood  hulls  of  which  are  of  less  scantling  than 
the  hulls  of  sailing  vessels,  it  is  consequently  only  applicable  to 
steam  vessels.  A  correction,  however,  in  this  respect  is  easily 
made  in  it,  by  which  the  comparative  buoyancy  of  the  two  kinds 
of  hulls,  in  regard  to  sailing  vessels,  is  equally  ascertained.  This 
is  as  follows  : — 

Difference  in  Scantling  allowed  in  Steam-vessels. 

With  regard  to  vessels  built  of  iron,  the  thickness  of  the  frame 
or  shell  is  the  same,  whether  they  be  propelled  by  the  power  of 
steam  or  sails  ;  but  this  is  not  the  case  in  respect  of  vessels  built 
oi  wood.  By  the  regulations  of  the  "  Society  of  Lloyd's  Regis- 
ter of  British  and  Foreign  Shipping,"  steam  vessels  under  300 
tons  may  have  the  scantlings  of  a  sailing  vessel  of  one-third  less 
tonnage,  and  those  above  300  tons  the  scantlings  of  a  sailing 
vessel  of  one-fourth  less  tonnage.  Therefore  this  difference  in 
scantling  allowed  in  steam  vessels,  amounting  generally,  both  in 
government  and  merchant  vessels,  to  about  one  inch  in  twelve 
inches  of  the  scantling  of  sailing  vessels,  or  8.333  per  cent,  must 
be  added  to  the  weight  of  the  wood  hulls  employed  in  the  above 
calculation,  in  order  to  bring  them  to  the  weights  of  the  hulls  of 
sailing  vessels.  Or,  in  other  words,  the  iron  hull,  with  regard 
to  sailing  vessels,  has  this  additional  buoyancy ;  and  as  16.16  per 
cent  of  the  weight  of  the  wood  hulls  of  steamers  is  only  14.9  per 
cent  on  the  weight  of  the  wood  hulls  of  sailing  vessels,  therefore — 

In  sailing-vessels  Iron  Hull  still  more  buoyant  than  in 
steam  vessels. 

In  the  case  of  sailing  vessels,  the  iron  hull  is  more  buoyant 
than  the  wood  hull  by  about  14.9  +  8.333  per  cent=  23.2,  or 
about  23  per  cent  of  the  weight  of  the  wood  hull. 


WEIGHTS    OF    IRON    AND   WOOD-BUILT   VESSELS.        55 

From  these  results  are  deduced  the  following  practical  conclusions  : 

1.  With  regaid  to  sailing  vessels. — It  is  known  from  experi- 
ence that  in  merchant  vessels  the  weight  of  the  wood  hull,  gene- 
rally speaking,  is  about  one-third  of  the  whole  displacement  of 
the  vessel,  and  that  the  weight  of  the  cargo  is  about  three-fifths 
of  that  displacement ;  therefore  the  weight  of  the  hull  is  to  the 
weight  of  the  cargo  as   1-3  to  3-5,  or  as  5  to  0 :   or,  in  other 
words,  the  weight  of  the  hull  is  about  5-9  the  weight  of  the  caigo. 
Therefore,  the  superior  buoyancy  of  the  iron  vessel  being,  as  be- 
fore shown,  about  23  per  cent  of  the  weight  of  the  wood  hull,  is 
five-ninths  of  23  per  cent,  or  about  13  per  cent  of  the  weight 
of  the  cargo. 

Hence,  if  two  sailing  vessels  be  built  from  the  same  drawing, 
one  of  wood  and  the  other  of  iron,  the  iron  vessel  will,  if  both 
vessels  be  loaded  to  the  same  draught  of  water,  cany  a  greater 
weight  of  cargo  than  the  wood  vessel  by  about  13  per  cent,  which, 
in  a  vessel  of  the  usual  form  of  about  700  tons  old  measurement, 
will  amount  to  about  135  tons  deadweight;  and  which,  if  not 
shipped  by  the  iron  vessel,  will  give  her  the  advantage  of  draw- 
ing about  sixteen  inches  less  water  than  the  wood  vessel. 

2.  With  regard  to  steam  vessels. — The  wood  hull  being,  as 
before  stated,  of  less  scantling  than  in  sailing  vessels,  its  weight 
will   be   less   in  proportion  to  the  cargo  than  in   sailing  ves- 
sels ;   whilst  on  the  other  hand  this  may  be  considered  as  quite 
neutralized  in  consequence  of  the  extieme  sharpness  of  form  in 
steam-vessels,  by  which  more  timber  is  expended  in  the  frame  in 
proportion  to  capacity  ;  consequently  the  weight  of  the  wood 
hull  in  steam-vessels  may,  as  in  sailing  vessels,  be  considered  to 
be  equal  to  about  five-ninths  of  the  weight  of  the  cargo.     There- 
fore the  superior  buoyancy  of  the  iron  steam-vessel,  as  before 
shown,  being  about  16  per  cent  of  the  weight  of  the  wood  hull, 
is  five-ninths  of  16  per  cent,  or  nearly  9  per  cent  of  the  weight 
of  the  cargo. 

Hence,  if  two  steam  vessels  be  built  from  the  same  drawing, 
one  of  wood  and  the  other  of  iron,  the  iron  vessel  will,  if  both 
vessels  be  loaded  to  the  same  draught  of  water,  carry  a  greater 
weight  of  cargo  than  the  wood  vessel  by  about  9  per  cent,  which, 
in  a  vessel  of  700  tons  old  measurement,  and  of  the  usual  steam 
vessel  form,  will  amount  to  about  70  tons  deadweight ;  and  which, 
if  not  shipped  by  the  iron  vessel,  will  give  her  the  advantage  of 
drawing  about  nine  inches  less  water  than  the  wood  vessel. 

The  advantage  of  iron-built  vessels  with  regard  to  the  power 
of  carrying  heavy  cargoes,  as  well  as  to  capacity  for  the  stowage 
of  light  merchandise  is  therefore  indisputable. 


56        FORMULA    TO   APPROXIMATE    REGISTER   TONNAGE. 

FORMULA    TO     APPROXIMATE     REGISTER     TON-' 
NAGE    UNDER   ANY   PROPOSED    DIMENSIONS. 

[Extracts  from  Mr    Moorsom's  Report,  published  in  the  proceedings  of  the 
"Institute  of  Naval  Architecture."—  London,  I860.] 

To  Shipbuilders  who  may  wish  to  know,  before  the  construc- 
tion of  an  intended  design,  the  approximate  register  tonnage  un- 
der any  proposed  principal  dimensions,  the  following  'formula 
(which  has  received  the  approbation  of  Messrs.  Martin  and 
Ritchie,  the  two  chief  surveyors  of  LloydTs,  who,  from  their 
great  experience  and  intelligence,  are  authorities  on  the  subject) 
will  be  found  useful,  as  it  gives  the  tonnage,  on  an  average,  gen- 
erally speaking,  within  about  2|  per  cent. 

Let  L  represent  the  inside  length  on  upper  deck  from  plank  at 

bow  to  plank  at  stern. 

"      B  represent  the  inside  main  breadth  from  ceiling  to  ceiling. 
"      D  represent  the  inside  midship  depth  from  upper  deck  to 

ceiling  at  limber-strake. 

*  T   \S  "R  \^  T") 

Then  the  register  tonnage  of  any  ship  will  be  equal  to  —  —  , 

multiplied  by  the  decimal  factor  opposite  the  class  in  the  follow- 
ing Table  to  which  she  belongs  : 

o  .7-   „  01-        5  Cotton  ailcl  Sugar  Ships,  old  full  form.  ...     -8 
Sailing  Ships.  ! 


SMps  Qf  the  pgent      ual  fom 

Steam  Vessels     <  Ships  of  two  Decks  ....................  '65 

and  Clippers.    {  Ships  of  three  Decks  ...................  -68 

v   ,  .                 j  Vessels  above  60  Tons  .................  -5 

Yachts.              <  Vessels,  small  ........................  -45 


RULE  TO  ASCERTAIN  THE  MEASUREMENTS  AND 
DEADWEIGT    CARGO    OF    SHIPS. 

A  brief  Explanation  of  the  Nature  of  the  Register  Tonnage  of  a 
Ship  as  ascertained  under  the  "  Merchant's  Shipping  Act,  1854" ; 
and  of  the  easy  means  it  affords  for  estimating,  approximately, 
the  Measurements  and  Deadweight  Cargo  of  Ships. 

1st.  The  Register  Tonnage  of  a  Ship  expresses  her  entire  in- 
ternal cubical  capacity  in  tons  of  100  cubic  feet  each  ;  so  that  it 


TO    ASCERTAIN    THE    DEADWEIGHT    CARGO    OF    SHIPS.     57 

is  only  necessary  to  multiply  such  tonnage  by  100,  and  the  entire 
internal  capacity  of  the  ship  in  cubic  feet  is  immediately  shown  ; 
and  from  which  an  owner  can,  by  making  such  deductions  for 
passengers,  provisions,  stores,  &c.,  as  the  circumstances  of  the 
particular  voyage  may  require,  arrive  at  the  net  space  in  cubic 
feet  for  the  purpose  of  cargo. 

2nd.  To  ascertain  approximately  for  an  average  length  of 
voyage  the  Measurement  Cargo  at  40  feet  to  the  ton  which  a  ship 
can  carry,  (as  many  owners  may  be  unwilling  to  trouble  them- 
selves with  the  above-mentioned  deduction,)  it  is  only  necessary 
to  multiply  the  number  of  register  tons  contained  under  her  ton- 
nage-deck, as  shown  separately  in  the  Certificate  of  Registry,  by 
the  factor  1J  and  the  product  will  be  the  approximate  meas- 
urement cargo  required. 

3d.  To  ascertain  approximately  the  Deadweight  Cargo  in  tons 
which  a  ship  can  safely  carry  on  an  average  length  of  voyage, 
(deadweight  bearing  a  certain  qualified  relation  to  internal  capac- 
ity,) it  is  only  necessary  to  multiply  the  number  of  register  tons 
under  her  tonnage-deck  by  the  factor  11,  and  the  product  will  be 
the  approximate  deadweight  cargo  required. 

4th.  With  regard  to  the  cargoes  of  Coasters  and  Colliers  as- 
certained as  above,  whose  short  voyages  require  but  a  small  equip- 
ment of  provisions  and  stores,  and  whose  frames  or  shells  are  of 
larger  scantling  in  proportion  to  their  capacity  than  in  the  larger 
classes  of  vessels,  about  10  per  cent  may  be  added  to  the  said  re- 
sults ;  while,  on  the  contrary,  about  10  percent  maybe  deducted 
in  the  case  of  the  larger  vessels  going  longer  voyages. 

5/A.  In  the  case  of  the  Measurement  Cargoes  of  Steam  Vessels, 
the  spaces  occupied  by  the  machinery,  fuel  and  passengers,  and 
cabin  under  deck,  must  be  deducted  from  the  space  or  tonnage 
under  the  deck,  before  the  application  of  the  measurement  factor 
thereto  ;  and  in  the  case  of  their  deadweight  cargoes,  the  weight 
of  the  machinery,  water  in  the  boilers,  and  fuel,  must  be  deduct- 


58     TO    ASCERTAIN    THE    DEADWEIGHT    CARGO    OF    SHIPS. 

ed  from  the  whole  deadweight  as  ascertained  above  by  the  ap- 
plication of  the  deadweight  factor. 

It  may  also  be  as  well  to  observe,  in  regard  to  this  latter  ques- 
tion of  weight-cargoes,  that  parties  are  agitating  as  to  the  desira- 
bleness of  placing  a  scale  of  tonnage  on  a  ship's  Certificate  of  Reg- 
istry, to  show  the  weight  of  cargo  carried  at  different  Alines  of 
flotation,  for  the  convenience  of  ship-owners,  brokers  and  masters. 
I  question,  however,  if  the  utility  of  this  object  is  at  all  commen- 
surate with  the  labor  and  difficulty  to  be  met  with  in  its  attain- 
ment ;  for  I  have  yet  to  learn  that  even  the  parties  themselves 
for  whose  interest  it  is  proposed,  desire  such  a  document.  More- 
over, as  the  information  to  be  derived  from  it  is  entirely  for  the  pri- 
vate purposes  of  the  ship-owner  and  his  agents,  and  can  be  fur- 
nished him  by  any  respectable  builder  or  surveyor  of  shipping,  it 
ought  to  be  so  procured  (if  such  information  be  necessary),  and 
most  certainly  not  at  the  public  expense  ;  an  expense  of  no  incon- 
siderable amount,  if  the  document  had  to  be  furnished  to  the 
whole  commercial  navy  ;  for  upon  a  moderate  calculation,  the 
number  of  ships  of  the  United  Kingdom  being  about  27,000,  it 
would  occupy  ten  or  twelve  practised  draughtsmen,  nine  or  ten. 
years  for  its  completion,  and  probably  two  or  three  others,  in  ad- 
dition, for  the  ships  annually  building.  Again,  a  ship's  certifi- 
cate of  registry,  on  which  it  is  proposed  to  place  the  scale  in  ques- 
tion, is  simply  a  document  of  nationality,  fiscal  tonnage,  and 
identity,  and  should  not,  in  my  opinion,  be  incumbered  with  other 
matter  not  strictly  relevant  thereto.  All  that  appears  to  be  re- 
quisite for  the  convenience  of  an  owner,  as  regards  particular 
point  of  weight,  is,  that  he  should  know  the  number  of  tons 
necessary  to  be  shipped  to  depress  or  sink  his  ship  to  the  extent 
of  one  inch  in  the  neighbourhood  of  the  load-water-line  ;  for  the 
weight  of  one  inch  immersion  varies  but  little,  practically  speak- 
ing, within  the  range  of  the  load  and  light  draughts  of  merchant- 
men ;  and  with  this  simple  information  he  can  be  supplied  by 
almost  any  respectable  shipbuilder  or  surveyor  at  any  port  of  the 
kingdom.  The  nature  of  this  information,  and  the  extent  of  its 
practical  conveniences,  are  shown  by  the  following  Table  : 


TO   ASCERTAIN    THE    DEADWEIGHT    CARGO    OF    SHIPS.    59 


SAILING  VESSELS. 

Gross 
Register  Ton- 
nage under 
Deck. 

Tons  Weight  due 
to  1  Inch  Im- 
mersion in  the 
neighbourhood  of 
Load  Line 

Tons  Weight 
to  1  Inch  in 
neighbourhood  of 
Light  Line. 

Duncan  Dunbar 

1200 

16.56 

14.56 

Holmsdale  .     . 

1100 

15.50 

13.95 

Suffolk   .     .     . 

850 

13.00 

11.59 

Dorothy       .     . 

700 

11.64 

10.29 

Harwood     .     . 

400 

7.42 

6.58 

Fidelity  .     .     . 

71 

2.44 

2.14 

Steam  Vessels  . 

Great  Eastern  . 

18915 

95.00 

87.00 

Persia     .     .     . 

3100 

30.00 

26.60 

Australasian    . 

2500 

24.35 

21.00 

Mauritius    .     . 

1500 

18.50 

16.29 

Christina    . 

700 

11.58 

10.93 

Grange  .     .     . 

400 

8.40 

7.82 

Thor.     .     .     . 

300 

7.55 

6.99 

261.94 

235.74 

235.74 

26.20  dif- 

ference  or  10  per 

cent  on  the  average. 

It  is  seen  from  the  above  Table  that  the  weight  due  to  one  inch 
immersion  at  the  two  different  draughts  of  load  and  light  lines 
vary  on  an  average  on  several  vessels  to  the  extent  only  of  about 
ten  per  cent ;  and,  therefore,  that  the  weight  which  would  sink  a 
vessel  one  inch  when  she  is  floating  at  her  load  line,  would  sink 
her  one-tenth  of  an  inch  more  when  floating  at  her  light  line- 
It  is  hence  manifest,  that  if  we  take  this  weight  as  that  which 
would  sink  a  vessel  one  inch  at  any  point  between  the  light  and 
load  draughts,  it  would  involve  a  mean  error  of  only  one-twentieth 
of  an  inch  to  one  inch,  or  at  the  rate  of  a  little  more  than  half  of 
an  inch 'to  a  foot, —  an  approximation  sufficiently  near  for  all 
commercial  purposes  (should  such  information  be  required)  con- 
nected with  the  loading  and  unloading  of  ships. 


GO  CENTRE    OF    GRAVITY    OF    DISPLACEMENT. 


CENTRE    OF    GRAVITY    OF    DISPLACEMENT. 

Method  of  ascertaining  the  Centre  of  Gravity  of  the  Displacement 
of  a  Vessel,  founded  upon  the  same  general  Process  as  the  Rule 
for  determining  the  Register  Tonnage. 

PRELIMINARY  OBSERVATIONS. 
Remarks  on  the  position  of  the  Centre  of  Gravity  of  Displacement. 

The  centre  of  gravity  of  displacement  is  a  most  important  ele- 
ment in  the  science  of  naval  construction.  On  its  being  properly 
situated,  both  as  regards  its  longitudinal  and  vertical  position, 
depends  the  acquisition  of  many  of  the  most  important  sea-boat 
properties  of  vessels.  The  celebrated  Chapman,  the  most  emi- 
nently practical  and  scientific  author  in  Naval  Architecture  with 
whom  we  are  acquainted,  says,  that  in  submitting  vessels  of  first- 
rate  character  for  their  velocities  and  easiness  of  motions  at  sea 
to  scientific  investigation,  he  invariably  found  the  centre  of  gravity 
of  displacement  to  be  situated  within  the  limits  of  the  l-100thand 
l-50th  of  the  length  of  the  plane  of  flotation  before  its  middle  point. 

A  practical  remark  of  this  nature  deduced  from  scientific  anal- 
ysis, in  connection  with  practical  observations,  from  such  an 
authority  as  Chapman,  must  be  of  considerable  value,  and  worthy 
the  attention  of  all  naval  architects. 

On  the  position  of  this  centre  of  buoyancy  depends,  also,  the 
position  of  the  common  centre  of  gravity  of  the  ship,  or  that 
important  point  around  which  all  the  rotatory  and  oscillatory 
movements  of  the  vessel  take  place  ;  for,  by  a  well  known  law  of 
hydrostatics,  a  body  floating  on  a  fluid  will  not  be  at  rest  till  its 
centre  of  gravity  and  that  of  the  displacement,  or  buoyancy,  are 
in  the  same  vertical  line.  Consequently,  if  the  position  of  the 
centre  of  gravity  of  displacement,  under  a  determined  line  of  flota- 
tion, be  not  in  the  same  vertical  line  with  the  common  centre  of 
gravity  of  the  ship,  she  will  necessarily  revolve  round  the  latter 
till  it  be  so,  altering  more  or  less,  as  the  case  may  be,  the  intended 
line  of  flotation;  and  which  can  only  be  preserved  by  some  differ- 
ent arrangement  of  the  cargo  or  equipment,  or  by  the  addition  of, 
otherwise  unnecessary,  ballast. 

It  being,  therefore,  desirable  on  all  occasions  of  the  construc- 
tion of  new  vessels,  to  know  whether  the  centre  of  buoyancy  be 
properly  situated,  the  following  easy  and  practically  correct 
method  for  ascertaining  it  (founded  on  the  principles  of  the  gen- 
eral process  of  the  Rule  for  the  admeasurement  of  tonnage)  will, . 
perhaps,  be  acceptable  to  those  who  may  wish  to  attend  to  this 
important  element  in  the  designing  of  their  vessels. 


CENTRE    OF    GRAVITY    OF    DISPLACEMENT. 


61 


It  may  be  desirable  first  to  explain  the  general  theorem  for 
ascertaining  the  common  centre  of  gravity  of  any  system  of  bod- 
ies, which  is  as  follows  : — 


Fig.  1. 


Pig.  2. 


• 


ART.  1.  —  It  is  known  (from  mechanics)  that  if  A,  B,  C,  D, 
&c.,  figs.  1  and  2,  be  the  weights  of  a  number  of  bodies  situated 
as  regards  their  respective  centres  of  gravity,  at  the  perpendicular 
distances  a,  b.  c,  d,  &c.,  from  any  plane  EF  given  in  position  ; 
then  the  perpendicular  distance  of  their  common  centre  of  gravity 
G  (0)  fr°m  tne  plane,  is  equal  to  the  sum  of  all  the  moments 
from  the  plane  divided  by  the  sum  of  all  the  weights  ;  that  is, 


A+B+  C4-JD-I-&C 


whole  weight. 


And  as  in  homogeneous  bodies  the  cubical  contents  are  in  pro- 
portion to  the  weights,  the  equation  is  equally  true  when  A,  B, 
C,  &c.  ,  represent  the  cubical  contents  of  such  bodies  ;  therefore 


G  G  = 


whole  cubic  contents. 


ART  2. — In  the  application  of  the  above  theorem  to  the  dis- 
placement of  a  ship,  we  must  consider  A,  B,  C,  &c. ,  as  xepresent- 
Bl  6 


62  CENTRE    OF    GRAVITY    OF    DISPLACEMENT. 

ing  consecutively  the  whole  of  the  equi-distant  transverse  areas,  or 
infinitesimal  laminae,  the  integration  of  which  make  up  the  whole 
displacement.  And  if  we  suppose  the  common  interval  between 
A,  B,  C,  &c.,  or  the  areas,  to  be  represented  by  ra,  and  the 
plane  E  F  to  be  situated  at  A,  or  area  No.  1,  as  shown  in  the 
Figs,  by  the  dotted  planes,  then  the  perpendicular  distance  a  =. 

0,  the  perpendicular  distance  b  =  m,  the  perpendicular  distance 
c  =  2  m,  and  d  =  3  m,  and  so  on.     Hence  by  substitution  the 
equation  becomes 

_  A  X  0  +  B  X  1m  +  C  X  %m  +  D  X  3ra  +  &c.  _ 
cubic  contents  of  displacement. 

(4XO  +  .BX1+CX2+DX34  &c-)  X  m 
cubic  contents  of  displacement. 

And  if  the  areas  multiplied  respectively,  as  here  shown,  by  0, 

1,  2,  3,  &c.,  be  termed  the  functions  of  the  areas,  the  equation, 
verbally  expressed,  will  then  be  as  follows  : — 

The  distance  of  the^ 

dispfac  °mentV1from  !    _  sum  of  all  the  functions  of  the  areas  X  common  interval. 

area  No.  1,   meas-  j   ~  cubical  contents  of  displacement. 

ured   on    the    load  ! 

water-line.  J 

Now,  the  integration,  or  sum  of  all  the  functions  of  the  areas, 
is  to  be  arrived  at  precisely  in  the  same  manner  as  the  summing 
of  the  areas  in  the  Rule  for  the  admeasurement  of  the  internal 
capacity ;  that  is,  (numbering  them  successively  from  forward  1, 

2,  3,  &c.,)  multiply  all  the  even  numbered  functions  by  4,  and 
all  the  odd  numbered  ones  by  2,  except  the  first  and  last,  and  to 
the  sum  of  these  products  add  the  first  and  last  functions,  and 
multiply  this  whole  sum  by  one-third  of  the  common  interval  be- 
tween the  areas,  which  gives  the  sum  of  all  the  functions  required  ; 
which,  as  the  above  equation  shows,  is  to  be  multiplied  by  the 
common  interval,  and  then  divided  by  the  cubic  contents  of  the 
displacement,  to  give  the  position  of  the  centre  of  gravity. 

Hence  the  last  equation  for  finding  the  centre  of  gravity  of 
displacement  in  its  extended  form,  becomes 

(Sum  of  even  No.  funds.  X  4  +  sum  of  odd  No.  functs. 

The  distance  of  cen-^        X^,  except  first  and  last  -f-  sum  of  first  and  last  functs.) 
tre  of  gravity  of  dis-  j        x  K  common  interval  X  common  interval 
placement  from  area  *• 


1,  measured on  f  cubical  content  of  displacement, 

load-water  line.         J 

from  which  the  following  general  formula,  for  convenience  of 
computation,  is  derived. 


CENTRE    OF    GRAVITY    OF    DISPLACEMENT.  63 

General  Formula  for  finding  the  Centre  of  Gravity  of  Displace- 
ment, supposing  the  Jlreas  of  the  Sections  to  be  already  found. 


Length  on  load-water  line  from  rabbet  of 
stem  to  rabbet  of  stern-post    -f-     = 
ft.  common  interval  between  areas. 

No.  of 
Areas. 

Areas. 
Sq.    Ft. 

Functions  f1^" 
ofAre«-j.2i 

Products. 

1 

XO 

|   1 

2 

XI 

!4 

8    !            JX2 

I2 

4 

X3 

!4 

5    1 

x4 

i1 

is  ^  of  com.  int.  betn.  areas. 


sum  of  all  the  functs.  of  areas. 
is  common  int.  between  areas. 


.  sum  of  moments 
and  — 


displacement. 


sum  of  moments  from  plane,  or 
area  1. 

=  distance  of  centre  of  grav.  from  area  1. 


Position  of  the  Centre  of  Gravity  of  Displacement  below  load- 
water  line. 

The  process,  as  has  been  illustrated,  for  ascertaining  the  posi- 
tion of  the  centre  of  gravity  of  displacement  in  a  longitudinal 
sense,  is  equally  applicable  to  finding  it  in  a  vertical  sense,  that 
is,  its  distance  below  the  plane  of  flotation. 

In  this  case,  the  horizontal,  instead  of  the  vertical  areas,  are  to 
be  employed  :  they  are  to  be  numbered  in  succession  from  above  ; 
the  plane  in  position  from  which  the  moments  are  to  be  calculated, 
being  considered  to  be  in  the  plane  of  flotation  or  area  No.  1. 


64  LOAD    DISPLACEMENT    OF    A   VESSEL. 


LOAD   DISPLACEMENT   OF    A    VESSEL. 

Method  of  finding  the  Load  Displacement  of  a  Vessel,  by  means  of 
the  Formula  for  the  Admeasurement  of  Tonnage. 

The  load  displacement,  one  of  the  most  important  elements  in 
the  construction  of  a  vessel  of  war,  being-  equal  in  weight  to  the 
entire  weight  of  the  vessel,  comprising  the  weights  of  the  hull, 
masts  and  yards  and  their  furniture,  armament,  and  entire  equip- 
ment, is  at  all  times  determined  with  the  greatest  nicety. 

The  load  displacement  being  equal  to  the  entire  weight  of  the 
vessel,  is  that  volume  of  water  which  is  displaced  by  the  body  of 
the  vessel  when  completely  ready  for  sea  ;  and  is,  consequently, 
bounded  by  the  load-water  line  :  it  is,  therefore,  manifest  that  we 
have  only  to  ascertain  the  exact  cubical  content  of  the  vessel,  ft? 
the  outside  form,  which  lies  under  the  load-water  line,  and  we 
have  the  true  load  displacement. 

The  length  of  this  portion  of  the  body  is,  therefore,  the  length 
on  the  load-water  line,  measured  from  the  outside  of  the  plank  at 
the  stem,  to  the  outside  of  the  plank  at  the  stern-post ;  and,  there- 
fore, in  the  application  of  the  plan  to  the  finding  of  the  cubical 
content  of  the  displacement,  it  is  this  length  which  is  to  be  di- 
vided into  the  required  number  of  equal  parts  instead  of  the  inter- 
nal length  at  the  deck,  as  prescribed  in  the  Rule  for  determining 
the  register  tonnage. 

The  transverse  areas  of  the  displacement  being  sections  of  the 
external  volume,  the  depth  at  each  area  is  taken  from  the  load- 
water  line  to  the  outside  of  the  plank  or  rabbet  at  the  keel,  instead 
of  the  internal  depths  as  prescribed  in  the  Rule  for  the  admeas- 
urement of  register  tonnage. 

In  all  other  respects  the  process  is  identical  with  that  of  the 
Rule,  except  that  the  cubical  content  is  to  be  divided  by  35,  (there 
being  35  cubic  feet  of  water  to  a  ton  weight,)  in  order  to  give  the 
weight  of  the  displacement  in  tons,  instead  of  being  divided  by 
100,  as  therein  prescribed,  for  the  register  tonnage. 

Although  it  may  not  be  so  necessary  in  the  designing  of  mer- 
chant ships,  as  it  is  with  vessels  of  war,  to  ascertain  the  exact 
weight  of  the  displacement  to  a  determined  draught  of  water,  yet 
there  are  occasions  when  an  easy  and  correct  method  for  this 
purpose  might  be  of  great  utility  and  convenience  ;  and  this  could 
only  be  effected  by  means  of  calculations  on  the  displacement, 
allowing  the  necessary  displacement  for  the  whole  weight  of  the 
vessel  completely  equipped,  in  addition  to  the  weight  she  might 
be  required  to  carry. 


CUBATURE  OF  THE  PYRAMID.  65 

CUBATURE    OF    BODIES    OF    WHATEVER    CON- 
FIGURATION. 

The  general  formula  for  the  admeasurement  of  the  capacity  of 
vessels,  is  equally  applicable  to  the  cubature  of  all  bodies  of 
whatever  configuration.  It  measures  the  capacity  of  the  vessel 
herself  not  more  correctly  than  it  will  measure  the  number  of 
cubic  feet  contained  in. one  of  the  angular  chocks  under  her 
beams,  or  in  one  of  the  variously  curved  timbers  of  which  her 
frame  is  composed.  Giving  thus  the  true  mensuration  of  all 
bodies  under  all  circumstances,  it  is  obvious  no  evasive  measure- 
ment can  result  from  it. 

It  will  be  seen  from  the  examples  given,  that  it  ascertains  the 
cubature  of  the  common  wedge,  of  the  paralMopiped,  of  the  pyra- 
mid, of  the  cone,  and  of  the  frustums  of  these  bodies,  &c.,  &c., 
however  insignificant  or  colossal  their  dimensions,  with  the  same 
geometrical  exactness ;  and,  thus,  may  be  said  to  form,  in  itself, 
a  complete  theory  of  practical  mensuration  for  bodies  of  all  shapes 
and  proportions. 

CUBATURE  OF  THE  PYRAMID. 

Application  of  the  General  Process  to  the  Cubature,  and  to  the 
finding  of  the  Centre  of  Gravity  of  Bodies  unconnected  with 
Naval  Architecture. 

To  find  the  cubical  contents  by  the  general  process,  three 
breadths  are  measured  ;  namely  one  at  top,  one  in  the  middle, 
and  one  at  the  base. 

Top       No.  1 breadth  0  ft Area    0  sq.  ft. 

Middle  No.  2 breadth  2  ft Area    4  sq.  ft. 

Base      No.  3 breadth  4  ft Area  16  sq.  ft.        » 

NOTE.— A  work  "  on  Tonnage,"  might  naturally  be  considered  as  investiga- 
ting only  such  matters  as  have  reference  to  this  particular  question  ;  and,  there- 
fore, as  other  matter  which  may  be  deemed  of  an  irrelevant  character  has  been 
Buper added,  some  reason  assigned  for  such  digression  from  the  special  object  of 
the  work  would  seem  to  be  called  for. 

It  may,  therefore,  be  staled,  that  this  supererogatory  matter  is  introduced  to 
show  the  general  applicability  of  the  new  process  to  all  professional  invest- 
igations connected  with  the  theory  of  Naval  Archheclure  ;  and  thus  to  prove 
that  its  utility  is  not  to  be  considered  as  applicable  solely  to  the  purposes  of 
tonnage. 

We  would  therefore  submit,  particularly  to  the  members  of  the  profession, 
the  advantages  to  be  derived  from  so  correct  and  general  a  theory  ;  and  by 
which,  the  merchant  Shipbuilder,  in  the  ordinary  practice  of  measuring  his 
ships,  will  necessarily  become  familiar  (if  he  is  not  already  so)  with  a  process 
affording  a  most  correct  and  easy  method  for  all  the  theoretic  inquiries  above 
alluded  10,  should  he  wish  to  render  these  advantages  available  in  the  pursuit  of 
improvement  in  the  forms  and  proportions  of  his  models. 


66 


CUBATURE  OF  THE  PYRAMID. 


Let  a  vertical  section  be  represented  as  passing  through  the 
axis  of  a  square  pyramid,  the  perpendicular  height  of  which  is 
twelve  feet,  and  breadth  of  base  four  feet. 

Let  the  perpendicular  height  be  divided  into  two  equal  parts. 
Then  the  breadth  of  the  base,  being  equal  to  four  feet,  the  middle 
will  be  found,  either  by  measurement  or  similar  triangles,  to  be 
equal  to  two  feet.  And  the  areas  at  the  apex,  middle  point  and 
base,  being  as  before  stated,  the  cubature  is  as  follows : — 

GENERAL  FORMULA  FOR   CUBATURE. 
Three  Transverse  Areas  being  given. 


Length  from  Apex  to  Base, 
12  ft.  -r-  2  =  6  ft,  the  common 
interval  between  areas. 

No.  of 
Areas. 

Multi- 
pliers. 

Areas 
Sq.  Ft. 

Products. 

1 

1 

0 

0 

2 

4 

4 

16 

3 

1 

16 

16 

32 
2is| 

of  6  feet,  com.  interval  betn.  areas. 

64  cubic  content  of  pyramid. 

Now,  it  is  known  (from  fluxions)  that  the  cubature  of  the 
pyramid  is  equal  to  the  area  of  the  base  multiplied  by  one-third 
of  the  perpendicular  height ;  that  is, 

16  x  (12  -r-  3)  =  64  cubic  content,  geometrically. 

Hence  it  is  seen  that  the  above  cubature  is  mathematically 
correct.  It  will  be  perceived  that  in  the  above  formula  one  term 
of  the  general  formula  of  the  Rule  for  the  admeasurement  of  ton- 
nage is  wanting — namely  the  odd  numbered  ordinates  multiplied 
by  2.  The  reason  of  this  is,  that  in  the  case  of  the  employment 
of  only  three  ordinates  there  are  no  odd  numbered  ordinates 
beyond  the  first  and  last. 

If  five  areas  are  employed  instead  of  three,  the  result  will  be 
precisely  the  same,  but  the  process  will  be  of  course  so  much  the 
longer. 


CENTRE  OF  GRAVITY  OF  THk  PYRAMID. 


67 


To  FIND  THE  POSITION  OF  THE  CENTRE  OF  GRAVITY  OF 
-  THE  PYRAMID. 

GENERAL  FORMULA  FOR.  FINDING  THE  DISTANCE  OF  THE  CENTRE  OF 
GRAVITY  FROM  AREA  No.  1. 


Three  Transverse  Areas  being  given. 


Length  or  Perpendicular  Height  of  Pyramid, 
=  12  ft.  -r-  2  =  6  ft.,  com.  int.  betn.  areas. 

No.  of 
Areas. 

Areas. 
Sq.  Ft. 

Functions 
of  Areas. 

Multi- 
pliers. 

Products. 

{TA 

0 

x  0 

0 

1 

0 

2 

4 

X  1 

4 

4 

16 

3 

16 

X2 

32 

1 

32 

o  S 


w  S 


Ills  II 

ills  iit 

SitU?*"  ii  *S 
>^S~5|6 


48 
2  is  £  of  6  ft.  com.  int.  betn. 

areas, 

96  sum  of  functions  of  areas. 
6  is  com.  int.  betn.  areas. 

576  sum  of  moments  from  Area 
No.  1,  or  apex. 

Then,  as  the  distance  of  the  centre  of  gravity  from  Area  1  is 
equal  to  the  sum  of  the  moments  divided  by  the  cubical  content, 
and  the  cubical  content  is  64  feet  (see  page  62),  we  have, 
576  -i-  64  =  9  ft.  the  distance  of  cent,  of  grav.  from  Area  1,  or  apex. 

Hence  it  is  seen  that  the  above  process  for  finding  the  centre 
of  gravity  of  a  body,  founded  on  the  general  process  is,  in  its  ap- 
plication to  the  pyramid,  geometrically  correct. 

THE   GENERAL   PROCESS  APPLIED  TO  THE  MEASUREMENT   OF 
A  PIECE  OF  TIMBER. 

The  process  will  be  found  to  be  equally  applicable  to  the  prac- 
tical cubature  of  all  other  bodies  as  to  that,  shown  in  the  pre- 
ceding example,  of  the  pyramid. 

Suppose,  for  instance,  the  measurement  of  a  piece  of  timber, 
having  plane  sides  contained  between  any  two  parallel  rectangular 
ends,  were  required. 


68 


MEASUREMENT    OF    TIMBER. 


Supposing  the  dimensions  at  the  ends  to  be  3  by  4  feet,  and 
5  by  6  feet,  and  the  length  30  feet. 

Measurement  by  General  Process. 

The  nature  of  the  process  always  requiring  an  odd  number  of 
equidistant  ordinates,  an  additional  area  to  those  at  the  ends  must 
consequently  be  taken  in  the  middle  between  them.  Measure, 
therefore,  a  breadth  and  thickness  at  the  middle  of  the  piece, 
which  will  be  found  to  be  five  feet  and  four  feet  respectively,  and 
therefore  the  area  at  the  middle  point  will  be  equal  to  20  square 
feet.  And  the  areas  at  the  ends  being  as  respectively  shown  in 
the  formula,  the  cubature  is  as  follows  : 


GENERAL  FORMULA. 

Length  80  ft,  -5-  2  =  15  ft.  the 
com.  int.  betn.  areas. 

No.  of 
Areas. 

Multi- 
pliers. 

Areas. 
Sq.  Ft. 

Products. 

1 

1 

12 

12 

2 

4 

20 

80 

3 

1 

30 

30 

C3  —00 

jfx 

-s«s 


I,  Jn. 

1  e**l 

I   t;-}-Ji  o 

§  l*»d| 

I  8*33 


122 

5  is  $  of  15  ft.,  com.  int.  betn.  areas. 

610  cubic  feet. 

Hence  it  is  proved  that  a  log  of  timber  of  this  form  is  measured 
by  the  general  process  with  geometrical  truth. 

Jf  the  timber  were  of  a  circular  form,  as  part  of  a  mast  or  yard, 
the  cubical  content  would  be  ascertained  with  equal  practical 
truthfulness  :  and  so,  likewise,  of  any  other  form,  provided  the 
areas  be  first  correctly  determined. 

If  the  log  should  consist  of  irregular  portions, — that  is,  if  it 
should  increase  or  diminish  abruptly  in  its  bulk  or  dimensions  in 
one  or  more  places  (as  is  often  the  case  in  rough  timber), — each 
such  portion  should  be  submitted  separately  to  the  process,  and 
the  several  results  added  together  for  the  whole  content. 


